Uncorrelated Inequalities: A Multiproxy Measure Suggests Reduced Household Disparity

Uncorrelated Inequalities: A Multiproxy Measure Suggests Reduced Household Disparity | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Uncorrelated Inequalities: A Multiproxy Measure Suggests Reduced Household Disparity Scott R. Hutson This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7983970/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract Extreme inequality has received increased attention in the social sciences since the 1990s, in part because of the harm it causes and in part because it is avoidable. Bolstered by the Gini coefficient, a quantitative measure of inequality that enhances comparative studies across time and space, archaeologists have expanded the study of inequality in recent years. While many studies of inequality in archaeology focus on architecture, multiproxy studies that operationalize a capabilities approach have gained popularity. A challenge of multi-proxy studies is that simply averaging Gini coefficients for multiple variables can misrepresent inequality in societies where variables for inequality are not correlated. This paper introduces the Combined Gini Coefficient (CGC) and applies it to a sample of archaeological case studies with extensive domestic excavations. The CGC helps disambiguate societies where variables for material wealth are aligned from societies where such variables are not aligned. In these latter societies, inequality is lower than estimates based on single or averaged variables. This finding is valuable when set within a broader comparative context because it shows that high inequality seen today is not natural and that ancient case studies are relevant. Inequality households Gini coefficient Maya Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Inequality has become a popular topic in archaeology. Part of this popularity derives from the conspicuous growth of inequality in contemporary societies (see background section below) and part from the embrace of a measure—the Gini coefficient—that reduces inequality to a single number, conveniently enabling archeologists to use data from various time periods and world regions in the service of cross-cultural comparison and synthesis (Bowles et al., 2010; Fochesato et al., 2019; Kohler et al., 2018; Kohler et al., 2025). In the Maya area, researchers tend to apply the Gini coefficient to architectural variables because extensive data on non-perishable stone buildings can be acquired relatively easily through the use of aerial laser scanning (lidar). But looking only at architecture can be problematic. Scholars such as Martha Nussbaum and Amartya Sen (1993) have argued that reducing measures of inequality to a single variable, such as income or monetary wealth, fails to capture a robust view of well-being in any particular society. In what has come to be known as the capabilities approach, well-being derives not just from money but from education, women’s rights, having a voice in governance, and more. Likewise, archaeologists have argued that well-being in the ancient past is also muti-faceted (Arponen et al., 2016; Drennan et al., 2010; Hutson, 2023; Munson and Scholnick, 2022; Twiss et al., 2024). This means that different households within the same society may value (and derive contentment from) different goals; some invest in elaborate houses, others in portable wealth, others in ritual. Thus, we need measures of inequality that embrace multiple variables and accommodate case studies where households that rank highly in some variables rank lower in others. Acquiring robust, multi-proxy evidence for inequality brings three challenges. First, it requires extensive yet costly household excavations. This challenge means that we will have much smaller sample sizes: the number of extensively excavated households per site is low and the number of sites with more than a few such households is small. Ideally, the households in each site’s sample should date to the same time period so that they are part of the same society. To avoid a palimpsest effect that muddies interpretation, households should also have relatively short occupation spans. Since my expertise is in the Maya region, I began this research by compiling Maya case studies. Sites with extensive, well-published excavations in domestic contexts include Uxul, Mayapan, Copan, and Tikal. I also included the southwest Asian settlement of Çatalhöyük because recent research at this site (Hodder, 2022; Kay et al., 2022; Twiss et al., 2024) has closely examined inequality along the lines that I specify below, providing a robust case study that enables comparison from a different part of the world. The second challenge is that simply calculating Gini coefficients for each variable and averaging them may not lead to an accurate measure of what Oka and coauthors (2018:73) call “general inequality,” particularly in cases where different variables are not correlated. As a hypothetical example, I will continue with the scenario stated above where disparate values lead some households to invest in elaborate houses, others in portable wealth, and others in ritual. Let us imagine that in this example, a settlement’s households each have relatively equal resources (minimal general inequality) but a third of them spend heavily on architecture, another third on personal adornments, and the final third on incense burners. Gini coefficients for each of these three variables (architecture, adornments, and censers) will be high. If, following Oka and coauthors (2018), we treat the average of these three Ginis (the Composite Archaeological Inequality index, or CAI) as a measure for studying trends in equality across societies, the high average Gini for this example cripples the effort to study trends because it misrepresents the fact that households in this settlement have relatively equal resources but expend them in different ways. This instance of misrepresentation merits further discussion as it permits a disambiguation of key terms. Inequality refers to the differential distribution of a valued resource. One can measure inequality for each valued resource (architecture, adornments, censers, etc.). General inequality refers to the degree to which multiple measures of inequality align. When most measures of inequality align, which is to say when some households are poor in most or all ways and others are rich in most or all ways, general inequality is high: resources as a whole are not evenly distributed. Well-being refers to the ability to fulfil desire. Since different people in the same society desire different things (and derive different amounts of happiness from the same quantity of a particular resource), inequality in the distribution of a single resource will not capture well-being (Sen, 1980). However, when general inequality is high, some households experience deprivation in most or even all possible ways, lowering well-being. Thus, well-being has a situational, not absolute, relation to inequality. To address the second challenge (that averaging Gini scores misrepresents societies where variables for inequality are not strongly correlated), I present the Combined Gini Coefficient (CGC). The CGC takes into account multiple variables and therefore fits the capabilities approach. Yet, unlike measures that average Gini coefficients for multiple variables (e.g. the CAI), the CGC helps distinguish societies in which different forms of inequality correlate with each other (households that score highly on one variable tend to score highly on most others) from societies in which inequalities are not correlated (households that score highly on one variable score less highly on others). Thus, the CGC provides a more accurate picture of general inequality in the past. Oka and coauthors (2018:90) caution that measures that take into account multiple variables for inequality, such as the CAI or the CGC, “cannot be taken as absolute measures of inequality.” Oka and coauthors are definitely correct since poor preservation of ancient lives prevents archaeologists from measuring all possible past inequalities. Yet, to the extent that archaeologists compare inequality from one site or time period to another, whether using a single variable (e.g. Kohler et al. 2025) or multiple variables (e.g. Oka et al., 2018), they are indeed presuming that their preferred measure acts as a “replicable measure of general inequality” (Oka et al., 2018:73). It therefore behooves us to find the most accurate measure possible, even if such a measure is not “absolute.” Further below, I demonstrate how the CGC works using data from the ancient Maya city of Chunchucmil and then apply it to the five case studies with extensive household excavations (Uxul, Mayapan, Copan, Tikal, and Çatalhöyük). The third challenge is that the ways that people choose to fulfil desires differ from settlement to settlement, making comparison difficult. Meeting this challenge requires measuring as many resources as possible. While no two settlements will have the same proxies for inequality, this does not mean that we will forever be comparing apples to oranges. The resources that people privilege from one society to another may differ, but the patterns in the distribution of resources can be compared. Thus, as long as the variables represent resources that are limited but desired, they can be admitted in a multi-dimensional study of inequality even if the variables are not the same from one settlement to another. The supplementary material provides the reasoning for why each variable used in this study can be understood is worth including as a potential measure of inequality. Given differences in the nature of the data from each site, the absolute numbers of variables per case study are not identical. Yet four of the five case studies with extensive excavations (Tikal being the exception) have either eight or nine variables. The hope is that this relatively consistent number of variables for each settlement will provide robust overall portraits of equality. The results of the analyses presented further below demonstrate a number of points. First, as predicted by the capabilities approach, different forms of inequality do not always align. In other words, it is not always the case that disparities “travel together, with one form of inequality facilitating or enhancing another” (Twiss et al., 2024:22). Second, the relationship between house size and combined measures of inequality can be unpredictable. These points echo univariate studies of inequality, using much larger samples, that have demonstrated that “different historical paths are empirically evident, and they reveal patterns and trends that are neither uniform nor linear” (Feinman et al., 2025:6). These conclusions are important because a refined measure of general inequality can challenge narratives about the durability of inequality. Researchers find that Gini coefficients for ancient, state-level societies are often similar to Gini coefficients for contemporary societies, thus making fairly high levels of inequality seem historically natural and unavoidable. The results from Uxul, Copan, and Mayapan show that ancient inequality was in fact lower than what we would assume on the basis of univariate Gini coefficients. In other words, high levels of inequality are not natural or unavoidable, a point on which I now elaborate. Background Increased academic concern with inequality dates back to the 1990s, when social scientists noticed dramatic increases in wealth disparities (Grusky and Kanbur, 2006). Governments, international organizations, and media paid increased attention by about 2015 when institutions such as the United Nations and the International Monetary Fund recognized inequality as a major threat to sustainable development (Philips, 2020:29-30). Though inequality within developed countries had been on the decline for the first three quarters of the twentieth century, due in part to progressive taxation, destruction of wealth from world wars, and burgeoning state investment in education, healthcare, social security, etc., it has grown sharply since the 1980s (Milanovic, 2016:4, Piketty, 2014, 2021:7-8). Within less-developed countries, globalization has led to explosive growth of inequality over the past four decades (Hung, 2021:7). In 2019, the wealth of the 26 richest people on the planet exceeded that of the poorest 50% of the world’s population combined (Philips, 2020:14). The COVID-19 pandemic exacerbated the situation (Franklin et al., 2020:757). The uptick in inequality gained attention not because of such gaudy trivia, but because of the deep and multi-faceted harm it causes. Wilkinson and Pickett’s (2009:494) literature review shows strong associations between greater income inequality and poor educational performance, low social capital, and higher rates of suicide, low birth weight, teen pregnancy, mental illness, homicide, violent crime, imprisonment, drug overdose, obesity, hostility, and racism. Nobel Prize Winner Joshep Stiglitz (2012:xii) writes that extreme inequality results in an "economic system that is less stable and less efficient, with less growth” and fewer opportunities for social mobility (see also Cunha Neves et al., 2016). High inequality imperils democratic governance (Deaton, 2014; Rau and Stokes, 2025) and threatens political stability as it empowers only a small sliver of the society and leaves a “working class suffering from stagnant or declining income” (Hung, 2021:12). High inequality often results in political violence, civil wars, revolutions, financial crises, and social movements. While tumultuous and bloody, such events tend to bring inequality back down (Piketty, 2022:10; Scheidel, 2017). One of the reasons why social scientists take great interest in the topic is that massive inequality is not inevitable. Rather, political ideology affects it (Stiglitz 2012). “Inequality does not follow a deterministic process…There are powerful forces pushing alternately in the direction of rising or shrinking inequality. Which one dominates depends on the institutions and policies that societies choose to adopt” (Piketty and Saez, 2014:841). If inequality is a “social, historical, and political construction” (Piketty, 2022:9), then people can deconstruct it. While generations of anthropologists and archaeologists have clarified that inequality is part of our primate heritage and can be found anywhere, this same body of research confirms that societies have devised creative strategies for constraining inequality (Ames, 2010; Graeber and Wengrow, 2021; Hodder, 2022; Weissner, 2002). As Ben Philips (2020:4) writes, “The problem we face in beating inequality is not that we do not know what needs to be done , it's that we haven't brought together the collective power to overcome those who are stopping it from being done." Indeed, cross-cultural comparison suggests that collective action can reduce inequality (Blanton and Fargher, 2008). This finding motivates recent research that attempts to understand the degree to which variation in how people govern themselves affects the amount of inequality in ancient societies is (Carballo and Feinman, 2016; Feinman et al., 2018, 2025 Hutson et al., 2023; Kohler et al., 2018). This paper contributes to comparative discussions of inequality by developing and applying a new method for quantifying degrees of inequality. Inequality is complex and protean. Different ways of measuring it lead to paradoxical conclusions. For example, one country’s inequality compared to another can diminish at the same time that inequality within that country increases (Hung, 2021; Sen, 2006:21). Poverty can climb drastically even when a country officially moves from “poor” to “middle income" (Philips, 2020:12). Nobel prize winner Amartya Sen illuminates a number of issues with the measurement of inequality and underscores the importance of using multiple proxies for wealth. In some societies, multiple proxies are closely linked, therefore allowing a single measure to characterize inequality more generally. Yet in other societies, one measure of wealth does not correlate with another. In these cases, we need a new way to characterize overall inequality if we wish to be able to make comparisons. Sen’s work has begun to influence archaeological studies of inequality (Arponen et al., 2016; Munson and Scholnick, 2022; Smith, 2015) and frames the methodological considerations in the following section. Aligned and Un-aligned Inequalities Put very simply, in his capabilities approach, Sen (1980) recognizes that using a single measure of inequality, such as income, often fails to capture variation in quality of life for two reasons. First, well-being is multi-faceted, involving basic concerns such as nourishment, clothing, and shelter but also outcomes that income does not directly capture, such as social respect, career fulfillment, political voice, and opportunities for women (Sen, 1993, 2006:35; see also Drydyk, 2005; Nussbaum, 2005; 2006). Second, within any particular society, individual people and groups “differ a good deal from each other in the weights they attach” to particular values and the contentment they derive from income or other physical goods (Sen, 1993:39; Stewart, 2005). If human development is therefore about expanding choices and growing opportunity, then any assessment of the human endeavor requires multiple measurements (Piketty, 2022:22). Sen’s argument helped shape the United Nations Development Programme’s (UNDP) Human Development Reports, which, beginning in 1990, recognized the importance of not just financial wealth, but also a society’s health, human rights, creativity, political freedom, and more (UNDP, 1990). The UNDP created the Human Development Index (HDI) as an explicitly multidimensional measure of the standard of living, combining income, literacy and life expectancy (Grusky and Kanbur, 2006:11). In archaeology, many studies of inequality focus narrowly on house size (Basri and Lawrence, 2020; Betzenhauser, 2018; Brown et al., 2012; Ellyson et al., 2019; Hutson et al., 2023; Kohler et al., 2025; Squitteri and Altawheel, 2022; Thompson et al., 2021). Focusing on house size has several advantages. Archaeologists in Mesoamerica often observe a correlation between house size and wealth (Folan et al., 2009; Haviland and Moholy-Nagy, 1992; Carmean et al., 2011; Tourtellot et al., 1992). According to Smith and coauthors (2014:312), houses of the rich are larger than houses of the poor for two reasons. “First, larger houses are more costly to construct, using more material, time, and labor, and thus show a positive association with household wealth. Second, wealthier households often construct larger and more elaborate residences to display their wealth or position.” Furthermore, if houses are larger because more people live in them or they have greater storage needs, these concerns also involve inequality since an increase in residents means greater access to labor and more storage means possession of more resources (Kohler et al., 2025). Another advantage of using house size is that it can often be measured without excavation, therefore enabling the collection of large samples at relatively low cost. Finally, house size enables standardized comparisons between sedentary societies across the world and across multiple time periods (Chase et al., 2023; Kohler et al., 2018). Yet focusing on house size alone also has drawbacks. House size does not always correspond with wealth (Hodder, 2016; Hutson, 2016:148-151; Kay et al., 2022:586) and may relate instead to the nature or household activities, previous construction not related to current occupants, the politics of labor organization, formation processes, and more (Hendon, 1992; Kay et al., 2022; Kuijt, 2024; Munson et al., 2023; Oka et al., 2018:71; Peterson and Drennan, 2018:44, 48; Peterson et al., 2016:214; Walden et al., 2023). Multi-proxy analyses mitigate an over-reliance on house size. They also help distinguish different kinds of inequalities, such as material (tangible resources such as tools and buildings), relational (social and political connections), and embodied (corporeal and intellectual expertise) (Bowles et al., 2010). A sample of recent multiproxy studies in archaeology includes Feinman and colleagues’ (2018) examination of obsidian, bone, house size, patio size, and terrace size in the Valley of Oaxaca, Nishimura’s (2023) exploration of 13 variables, including architecture, artifacts and burials, from Bronze Age Titriş Höyük, Turkey, and Wright’s (2014) and Twiss and collaborators’ (2024) examinations of over a dozen variables at neolithic Çatalhöyük (see also Fochesato et al., 2019; Stone, 2018; Oka et al., 2018). Multiproxy studies in which patterns from one variable differ from patterns in another variable have the potential to explore the complexity of inequality in the spirit of Sen’s capabilities approach. For example, Munson and Scholnick’s (2022; see also Munson et al., 2023) study of burials at Altar de Sacrificios shows that there was very little inequality in terms of skeletal health, reflecting embodied well-being, but substantial inequality in terms of personal adornments, reflecting material wealth. Proxies for social connectedness fell in between material wealth and embodied well-being. Kohler and Higgins’ (2016) comparison of house size and storage space among ancestral Puebloans suggests to them a distinction between wealth and income. Ortman and colleagues (2025) argue, on the other hand, that house size is a better indicator of income than of wealth. Studies from Çatalhöyük show, among other things, that the houses with the most burials and symbolic elaboration (such as bucrania) are not the houses with the most surface area or the most storage space (Hodder, 2022:623; Kay et al., 2022). The work of Robert Drennan and Christian Peterson (2006, 2012; Drennan et al., 2010; Peterson and Drennan, 2018; Peterson et al., 2016) provides a sustained engagement with different kinds of inequality and the multiple proxies required to tease these out. At the Hongshan (4500-3000 BCE) site of Fushanzhuang, in the Chifeng region of China, they find two separate but uncorrelated hierarchies: one of wealth—as indicated by finely made and better finished ceramics—and one of status (Drennan et al., 2010:59) or prestige (Peterson et al., 2016:209)—as indicated by decorated pottery. Likewise, at Yuchisi, a Late Dawenkou (3500-2600 BCE) central place in Anhui province, China, personal adornment, which Peterson and coauthors equate with prestige, does not correlate with serving vessels and fine-paste ceramics, which they equate with wealth. On the other hand, during the Guadalupe phase (900-700 BCE) at Fabrica San Jose, a village in the Valley of Oaxaca, “status and wealth are intertwined…and this integrated system of ranking emerges strongly from the household evidence” (Drennan et al., 2010:62). Likewise, at Dadiwan, a large, Late Yangshao period (4000–3000 BCE) settlement in Gansu province, China, households with greater wealth also have greater indicators of status; wealth and status were unified into a single, clear axis (Peterson et al., 2016:206, 210). The contrast highlighted by Drennan and Peterson—societies where variables for wealth and prestige align versus societies where they do not—also exists in the Maya area. A clear example comes from Tikal and Chunchucmil, a pair of cities which reached similar populations (about 40,000 to 45,000 for Tikal [Haviland, 1970:193, 1972:138, 2003:129]; between 31,000 and 47,000 for Chunchucmil [Hutson et al., 2017]) at approximately the same time (between 550 and 770 CE for Tikal [Haviland, 2003:124-129; 2014:131] and between 400 to 630 CE for Chunchucmil [Jiménez et al., 2017]). Both cities feature central marketplaces (Jones, 2015; Dahlin et al., 2007). At Tikal, house size, access to obsidian, access to seashell, and assemblage diversity and are all positively correlated (Hutson, 2020:72-3). At Chunchucmil, residential floor area, architectural volume, access to obsidian, fancy pottery, and other resources are not correlated (Hutson, 2020:72-3). In line with Sen’s capabilities approach, the lack of correlations at Chunchucmil can be interpreted as a case in which different households had the freedom to pursue different pathways to well-being. Inequalities existed, but they are “domain-specific” (Kay et al., 2022:584) at Chunchucmil. While some households invested more in material wealth, others invested more in social wealth. To quote Munson and Skolnick (2022:4), "what people value in life (e.g., what they strive ‘to be and do’) differs not only between societies but within them as well." In cases like Fábrica San José and Tikal, richer households specialize in craft production. Excavations at Early Bronze age III (2850-2550 BCE) Numayra, Jordan, and 7 th century CE Cerén, El Salvador, specialization leads not to clear differences in well-being among households but rather horizontal differentiation and degrees of interdependency (Oka et al., 2018:87; Sheets, 2020). Quantifying overall inequality when inequality is domain-specific: The Combined Gini Coefficient (CGC) Whereas sites like Fábrica San Jose, Tikal, and Dadiwan exhibit clean, homogeneous hierarchies, the findings at Fushanzhuang, Yuchisi, Chunchucmil, Numayra and Ceren exhibit domain-specific inequalities that are not correlated, akin to “a rich mosaic of varied relationships—cooperative, competitive, or conflictive” (Peterson and Drennan, 2016:220). Inequality among households in the second list of sites is not as pronounced as inequality in the first list of sites. But how do we quantify inequality more generally at sites where inequality is domain-specific; e.g. settlements where different measures of well-being are not correlated? As mentioned in the introduction, Oka and colleagues (2018) propose a generalized measure of inequality that they call the Composite Archaeological Inequality index (CAI). The CAI is the geometric mean of the Gini coefficients of all available variables. By aggregating multiple measures of well-being, the CAI takes inspiration from the HDI, and therefore operates under the logic of Sen’s capabilities approach. Yet in cases like Yuchisi and Chunchucmil, where variables for inequality are not correlated, the CAI overestimates the degree of inequality. For example, if the Gini coefficients for fine pottery, access to exotic trade goods, and volume of domestic architecture are .52, .56, and .60, the CAI/geometric mean (as well as the arithmetic mean) would be .56. But if the households with the most fine pottery do not live in the most voluminous houses and the households with access to abundant trade goods possess relatively little fine pottery, etc., averaging the Gini scores misses the fact that material wealth is broadly dispersed across many households. This dispersion means that overall inequality would be lower than what the CAI suggests. Drennan and Peterson (2006) resolve this problem through multi-dimensional scaling, which creates visual representations of how individual households differ from each other along multiple axes of variation. While useful for understanding the rich mosaic of human striving at a particular settlement, multi-dimensional scaling does not enable quantitative comparison of generalized levels of inequality from one settlement to the next. The method proposed in this paper—the Combined Gini Coefficient, or CGC—allows for such comparison. Like most previous studies, this method uses the domestic compound (understood to be the archaeological remains of a household) as the unit of analysis. Each domestic compound has a value for each variable (house size, access to fancy pottery, etc.) whose distribution can be indicate inequality. For each variable, all variates are converted into scores between 0 and 100, such that the domestic compound with the highest value for a variable receives a 100 for that variable. After converting variates to scores between 0 and 100 for each variable, each domestic compound’s scores are summed and a Gini coefficient is calculated from the sums of scores. I will demonstrate the CGC method using data from six variables measured on 113 domestic compounds at Chunchucmil. The first variable, amount of obsidian, is a potential measure of wealth since obsidian is a long-distance trade good (the nearest source is over 600 km away as the crow flies) that requires resources to acquire. The values for this variable range from 0 to 18.9 grams per kg of pottery. A household with no obsidian would get a score of 0. The household with 18.9 grams of obsidian per kg of pottery—S6W4b (Operation 116)—receives a score of 100. A household with 6.3 grams of obsidian per kg of pottery, which is a third of the way between 0 and 18.9, would receive a score of 33.3. The values for the second variable, the amount of fancy pottery (measured in kg per total kg of pottery), range from 0 to 10.5. Domestic compound S6W4b happens to have no fancy pottery, thus receiving a score of 0. Moving to a third variable, volume of architecture, values range from 15.8 to 5337.6 m 3 , such that 15.8 converts to a score of 0.003 and 5337.6 converts to a score of 100. S6W4b has a volume of 298.6 m 3 , which falls near the low end of the range, and converts to a score of 5.1. Following the same procedure, S6W4b would receive scores for the remaining three variables (surface area of houses, amount of metates, and amount of depressions). S6W4b’s scores for the six variables would then be summed, as would the scores for each of the other 112 domestic compounds. The Combined Gini Coefficient (CGC) for these 113 scores, each of which combines six variables, is 0.357. This particular Gini score—0.357—is remarkable given that the Gini scores for each of the six variables range from 0.465 to 0.725. The arithmetic mean of these six Gini scores is 0.556, while the geometric mean (Oka and coauthors’ CAI) is 0.550 (see table 1). Thus, the CGC, which is attentive to domain-specific inequalities, shows overall inequality to be substantially lower than when calculated simply by averaging Gini scores. I argue that the CGC is more accurate because, unlike the arithmetic or geometric (CAI) averages of Gini scores, it takes into account cases in which variables for well-being are not correlated with each other: cases where different forms of inequality don’t “travel together” (Twiss et al. 2024). Finally, does the CGC allow comparison among different settlements? This question re-iterates the third challenge that I mentioned in the introduction. Even within the same region, artifact assemblages and other resources may differ across time and space such that variables for material well-being may differ from one settlement to the next. Thus, since the CGCs for different sites will contain different sets of variables, it would seem that comparing CGCs commits the error of not comparing like with like (Chase et al., 2023). Yet it would be dangerous to assume that the same variables that index inequality at one settlement necessarily index inequality for all settlements in the comparison. As an example, access to obsidian prismatic blades was unrestricted within Late Classic Copan (Aoyama, 2001; Hendon, 1991:909), with most households producing their own blades (Mallory, 1984). Blade counts should therefore not be used in the portfolio of variables used to measure overall inequality at Copan. At sites located much further from obsidian sources, however, obsidian can be more limited, making it an admissible variable when exploring patterns of inequality. In this paper, many variables pertain to what Bowles and coauthors (2010) would refer to as material wealth. A few could be argued to have a relational aspect in addition to a wealth aspect. For example, the number of sources of exotic shell to which a household had access at Çatalhöyük may index the number of trade partners. Likewise, a few variables have wealth, relational, and embodied aspects: musical instruments and incense burners at Uxul presume performative and/or ritual knowledge and skills learned from others that become embodied in individuals. The strength of the CGC is that it attends to different ways of life but includes as many variables as possible in order to produce a more generalized snapshot of inequality. Results: Applying the Combined Gini Coefficient The shortcoming of the Chunchucmil example in the previous section is that most of the data comes from test pitting. Of the 113 residential groups in the sample, the average surface area of excavation was 7.5 m 2 (this figure does not include the few groups that received horizontal excavations). While Peterson and co-authors (2016:201) maintain that relatively minor excavations can “provide large samples of artifacts for comparative analysis”, other studies show that test pitting, as opposed to broader excavations, can miss important aspects of ancient household organization, production, and consumption (Masson and Peraza Lope, 2014:336). Thus, I want to focus the CGC on case studies with extensive household excavations. The obvious trade-off is that, due to the high cost of extensive broad-scale excavations, the case studies with well-reported household data have relatively small sample sizes of excavated houses. The current study includes ten well excavated house compounds from Uxul, eight from Mayapan, nine from Copan, and 13 from Çatalhöyük. I also include 34 domestic contexts from Tikal; these contexts are not as thoroughly excavated as those at Uxul, Mayapan, and Çatalhöyük, but are better excavated than most contexts at Chunchucmil. Fortunately for archaeologists constrained by the difficulty of conducting broad-scale household excavations, Fochesato and colleagues (2019:865) show that “relatively small samples from much larger populations yield reasonably accurate and precise estimates of the Gini coefficient.” Uxul, located in the Central Maya Lowlands of Campeche, Mexico, was a secondary center heavily influenced by enormous Calakmul, located 32 km to the northeast (Grube et al., 2012). While Uxul has occupation dating to the first Millennium BCE, excavations reveal that most of its structures were built and occupied between 650 and 750 CE (Barnard, 2021:57), when it housed several thousand people. Thus, the residential contexts have reasonable chronological control, though the sample is likely not representative of the site as a whole given that no small residential compounds were excavated extensively. Drawing on data published by Barnard (2021), I included nine variables in the analysis: residential surface area, architectural volume, and amounts of obsidian, greenstone, polychrome pottery, shell artifacts, incense burners, figurines, and musical instruments (table 2, Supplementary table 1; see Supplementary Materials for discussions of these variables and those in the rest of the sites below). None of these variables are significantly positively correlated (see table 3). I therefore anticipate a low CGC. Indeed, while the average of the Gini coefficients for these nine variables is 0.496 (CAI is also 0.496), the CGC is 0.238 (table 1; figure 2a, 3). This result agrees with the finding that domestic compounds with substantial architecture at Uxul did not have better access to ceremonial facilities, water sources, and other services (Barnard, 2021:172-173), a finding which contrasts with common patterns (Dennehy et al., 2016; Stanley et al., 2016). If smaller residential compounds were excavated and included in the sample, the CGC would probably be higher, but so would the Gini scores for individual variables. Mayapan, located in the northern Maya lowlands of Yucatan, Mexico, was the capital of a political confederacy from 1250 CE to 1450 CE and the largest Maya center of its time, reaching a population of about 15,000. Broad-scale excavations of eight domestic compounds show relatively short occupations and the sample of eight is representative in the sense that it includes what the excavators argue to be both elites and commoners, some with craft specialization and some not. Drawing on published data (Masson and Peraza Lope, 2014; Masson et al., 2021), I included nine variables in the analysis: residential surface area and amounts of obsidian, chert, chert points, fancy pottery, imported pottery, ritual pottery, shell artifacts, and metal artifacts (table 4, supplementary table 2). Table 5 shows the 36 correlation coefficients for these variables, of which only three are significantly positive. The average of the Gini coefficients for these nine variables is 0.491 (nearly identical to Uxul’s average), with a CAI of 0.472 (table 1). In contrast, the CGC is 0.155 (figure 2b, 3). This low CGC falls in line with an earlier study suggesting minimal inequality at Mayapan (Brown et al., 2012) and would be expected given the weak correlations between variables. Çatalhöyük is a densely packed seventh millennium BCE settlement located on the Konya plain in Turkey. Its large number of inhabitants (up to a few thousand), make it anomalous for its time. It lacked features of Old World cities from later time periods, such as centralized political and religious institutions. Hodder (2022) has argued that egalitarian leveling mechanisms constrained aggrandizers who lived in the more elaborate buildings. Twiss and coauthors (2024) present extensive data from three phases at Çatalhöyük. I focus on the Middle Occupation phase (6700-6500 BCE), which has by far the largest sample (n = 13) of extensively excavated houses. I used eight variables, including number of grinding tools, paintings, faunal installations, human burials, grave goods, exotic shells, exotic shell sources and exotic stone beads (table 6, Supplementary table 3). Of the 13 houses, surface area measurements were available for only 11. Thus, although I calculated a Gini for surface area (see table 1), the variable was not included in the calculation of the average Gini scores, the CAI, and the CGC. The average Gini score is 0.592 (CAI is 0.563) with a CGC of 0.447 (figure 2c, 3). The relatively high CGC reflects the fact that 39% (11 of 28) of correlations between variables are significantly positive (see table 7). Tikal, located in Peten district of Guatemala, is a very large Maya city with regional political clout rivalled only by the Kaan dynasty of Calakmul/Dzibanche. Data come from domestic excavations well-reported by Haviland (2014). As noted above, domestic contexts at Tikal were not as broadly excavated compared to Uxul, Copan, Mayapan, and Çatalhöyük. Furthermore, whereas the domestic occupations at the other sites generally span 200 years or less, many of the domestic compounds at Tikal had much longer occupations, amplifying a palimpsest effect that injects more caveats into the interpretation of inequality. Another potential problem is that Tikal has only half the variables as the other four sites with extensive excavations (composite indices tend to stabilize with more variables: Oka et al., 2018:90). Finally, the excavation sample only includes non-elite domestic compounds (recall that the Uxul sample is biased toward large compounds). Despite these downsides, I include Tikal in the case study because, unlike the other Maya cases, its variables for material well-being are more strongly correlated (see Supplementary table 4). In other words, variables for inequality travel together. We would therefore anticipate a higher CGC. As expected, the CGC for Tikal is 0.481 (table 1, figure 2d), higher than the other CGCs (figure 3), and closer to the average of its Gini scores, 0.598. Such scores would be even higher if the excavation sample contained elite households. Given the other shortcomings of the Tikal case (longer occupation, fewer variables, less extensive excavation), the result for Tikal may not be as trustworthy. Copan, located in the southern lowlands in western Honduras, is one of the best-known Maya sites. It was a city state capital with a peak population of 20,000 people and an extensive corpus of hieroglyphic inscriptions centered on a dynasty with at least 16 consecutive kings. Copan benefits from several projects focused on household archaeology (for example Landau, 2016; Webster and Gonlin, 1988). I use data from the Proyecto Arqueológico Copan II, directed by William Sanders from 1981 to 1985, because it featured complete and well-published excavations of households from all four status ranks, all within the city and all dated to the Late Classic Coner Phase (650-820 CE). The sample consists of nine patio groups (see Supplementary table 5). While some of these groups are part of larger architectural compounds, such as 9N-8, the “repeated occurrence” of basic household activities at each patio group “suggests that each patio functioned as a separate social-residential unit” (Hendon, 1991:904; see also Hendon, 1987: 488-489; Abrams, 1994). I used nine variables: residential surface area, architectural labor investment, extent of sculpture, imported fancy pottery, quantity of portable ornaments, figurines, bifacial projectile points, worked bone and proportion of basalt grinding stones/metates (table 8). I expected these variables to be correlated given that Fash (2005:96) notes that the “quality of the architecture, graves and tombs, and associated domestic artifacts generally correspond quite well” with the size of domestic compounds at Copan (see also Richards-Risetto, 2023). However, beyond the well-known, strongly positive correlations between architectural labor investment and residential surface area, and architectural labor investment and sculpture, only four of the remaining 34 potential correlations were statistically significant (table 9), and these remaining correlations are not intuitive (for example, number of figurines and bifacial points). Given the general lack of alignment between variables, the CGC was significantly lower than the average of the Gini scores for the nine variables (Table 1, Figure 3). Discussion and Conclusions When put into broader context, the CGCs for the five sites with extensive household excavations reveal a number of points about inequality. The first point is the different ways that inequality manifests itself. Figure 3 shows this clearly. The arithmetic average for the Gini scores of the variables for all sites are somewhat similar, ranging from 0.422 to 0.598. Yet this apparent similarity conceals the fact that in cases like Uxul, Copan, and Mayapan, the full range of resources are much more equitably distributed, as revealed by the relatively low CGCs. In other words, due to weak correlations among variables at Mayapan, Copan, and Uxul, households with a lower-than-average house surface area, for example, do not necessarily have lower-than-average shares of fancy pottery. In this way, variation in one resource counteracts variation in another measure, evening out and dampening overall inequality. On the other hand, at Tikal, patterns in one measure corroborate patterns in other measures, thus amplifying inequality across the board; households that score highly for one measure tend to score highly in other measures. Yet, as discussed above, aspects with the Tikal data set undercut confidence in the results for this site. Regarding Copan, Uxul and Mayapan, one might wonder how it can be that variables tied to material resources show no correlation. A straightforward explanation is that people have similar amounts of resources but choose to invest them in different pursuits. For example, if it takes wealth both to build a larger house and to acquire fancy pottery, these two variables can be uncorrelated if some households choose to invest resources in architecture and others choose to invest resources in pottery. Following Amartya Sen (1980) and Ted Fischer (2014), there might be multiple ways to find fulfilment within a particular society. Different people might value different pursuits, resulting in a lack of correlation. In such a case when variables for inequality do not travel together and the CGC is lower, general inequality is also lower, meaning that well-being is more broadly distributed. When general inequality is greater, many people will have very few resources to begin with, while others will have lots of resources. In this situation, reminiscent of Tikal, variables for different resources are more likely to be correlated and larger proportions of the population would have lower levels of well-being. Insofar as the CGC suggests a generalized picture of well-being and inequality, the results show a continuum between lower and higher overall inequality (figure 4). The results also show that surface area of architecture does not help predict overall inequality. Figure 3 shows that, among the Maya sites, the CGCs range widely but the Ginis for surface area are nearly identical, with the exception of Copan. In this small sample, surface area Ginis tend to over-represent inequality. Expanding the sample of surface area Gini coefficients to the 15 sites reported by Chase and coauthors (2023) shows that domestic surface area in the Maya area varies substantially, from 0.32 to 0.7, with an average of 0.46 (Figure 4). This average is similar to the average Gini for house surface area for 155 sites in Mesoamerica more broadly (Figure 4; Kohler et al. 2025). For Çatalhöyük, the domestic surface area Gini under-represents inequality. Though Çatalhöyük has been described as an egalitarian settlement that lacks some of the features of later settlements that are unquestionably urban, its CGC is in fact higher than cities like Uxul, Copan, and Mayapan. Thus, different measures of inequality traveled together at Çatalhöyük to a greater degree than at the Maya sites. While fine-grained analyses at Çatalhöyük “suggest a society grappling with the tensions between maintaining egalitarian norms and evolving social complexities” (Twiss et al., 2024:25; see also Wright, 2014), the CGC comparisons suggest Çatalhöyük may have been less egalitarian than some of the urban, politically centralized Maya settlements in this study. Alternatively, one might argue that the CGCs are misleading because each variable has the same weight. This critique is understandable for Copan where a variable such as architectural labor investment should probably be given more weight other variables. For example the resources used to build patio 9N-8a likely exceeded the resources needed to acquire a large proportion of basalt metates or bone ornaments, yet these two variables carry the same weight. Figure 4 places the CGCs in a more recent and global context of capital ownership. The intensive agriculturalist Gini of 0.57 reported by Shenk and coauthors (2010) represents an average of land and livestock Gini coefficients from four historic societies: East Anglians, Kipsigis, Krummhörn, and Yomut. The three recent Ginis for capital ownership in Scandinavia (0.58), Europe (0.67) and the United States (0.73) are taken from data presented by Piketty (2014). Though capital ownership captures wealth inequality more accurately than measures of inequality based on income from labor, it suffers from the shortcoming of all single proxy measures: many other factors beyond capital (freedom of artistic and political expression, availability of education, etc.) contribute to well-being. Nevertheless, it is notable that these Ginis are higher (often beyond the 95% confidence interval) than the CGCs from some of the ancient societies in this study. This is important because studies that largely limit samples of “preindustrial” societies to the 18 th and 19 th centuries risk drawing the oversimplified conclusion that “income inequality in pre-industrial countries today is not very different from inequality in distant pre-industrial times” (Milanovic et al., 2011:268). Once again, contemporary analysts can learn from ancient societies. Taken together, the data from Figure 3 suggest that inequality of material well-being as represented by the CGCs in some ancient Maya societies is over-estimated by existing Gini measures while the data in Figure 4 suggest that inequality in some ancient Maya societies was significantly lower than in other societies. Admittedly, Uxul’s CGC would be higher if the excavation sample included more small houses and Tikal’s CGC would be higher if the sample included more large houses. Nevertheless, the results and comparisons presented in this paper underscore the need for a method for disambiguating societies in which variables for well-being are correlated from societies in which they are not. The CGC provides this method while also suggesting the existence of relatively low levels of inequality even in urban, state-level societies. In the context of research that shows the devastating effects of growing inequality, this latter finding adds yet another voice challenging the notion that high inequality is inevitable. While the small sample sizes in this paper demand humility and caution, the hope is that the paper will stimulate methodological experimentation in other multi-proxy data-sets from broadly excavated domestic contexts. Statements and Declarations The author has no competing interests to declare. No funding was received for conducting this study. 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G., & Pickett, K (2009). Income inequality and social dysfunction. Annual Review of Sociology 35, 493-511. Wright, K. I. (2014). Domestication and inequality? Households, corporate groups and food processing tools at neolithic Çatalhöyük. Journal of Anthropological Archaeology 33, 1-33. Tables Tables 1 to 9 are available in the Supplementary Files section Additional Declarations No competing interests reported. Supplementary Files Supplementaymaterials.docx Tables.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 23 Jan, 2026 Reviews received at journal 18 Jan, 2026 Reviews received at journal 08 Dec, 2025 Reviews received at journal 07 Dec, 2025 Reviewers agreed at journal 09 Nov, 2025 Reviewers agreed at journal 05 Nov, 2025 Reviewers agreed at journal 05 Nov, 2025 Reviewers invited by journal 04 Nov, 2025 Editor assigned by journal 04 Nov, 2025 Submission checks completed at journal 30 Oct, 2025 First submitted to journal 29 Oct, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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1","display":"","copyAsset":false,"role":"figure","size":621919,"visible":true,"origin":"","legend":"\u003cp\u003eMap showing location of Maya sites mentioned in the paper\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7983970/v1/9d29359061518fde0cd10e60.png"},{"id":96243306,"identity":"8e96f7e9-5ea2-4a99-8f7f-9c23f940680b","added_by":"auto","created_at":"2025-11-19 07:16:01","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":174729,"visible":true,"origin":"","legend":"\u003cp\u003eLorenz curves for case studies in this paper\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7983970/v1/82f57b5988f87bc96f815f9c.png"},{"id":96244765,"identity":"9536ffd4-4207-4591-98ca-50dc63f464f3","added_by":"auto","created_at":"2025-11-19 07:19:12","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":46277,"visible":true,"origin":"","legend":"\u003cp\u003eCGCs with 95% confidence intervals in the context of average Ginis and surface area Ginis from the same sites\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7983970/v1/b0172501576e3c367cba5163.png"},{"id":96243207,"identity":"ed822179-1a6d-4f5a-b456-85967b913880","added_by":"auto","created_at":"2025-11-19 07:15:50","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":55886,"visible":true,"origin":"","legend":"\u003cp\u003eCGCs with 95% confidence intervals in comparative context (other data taken from Kohler et al., 2025; Chase et al., 2023; Bowles et al., 2010; Piketty, 2014)\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7983970/v1/56d69d5db086af33a2b36244.png"},{"id":96255364,"identity":"33a9c175-5a45-4c3a-87ea-35e05a42c611","added_by":"auto","created_at":"2025-11-19 07:48:35","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1220906,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7983970/v1/c93bf178-fa8b-4da3-9b17-057f778d35df.pdf"},{"id":95939300,"identity":"9364e3d4-3429-4013-bd01-5ae64a61cf22","added_by":"auto","created_at":"2025-11-14 16:07:16","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":174399,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementaymaterials.docx","url":"https://assets-eu.researchsquare.com/files/rs-7983970/v1/e166cbdca35f1e13cd9b360d.docx"},{"id":95939287,"identity":"a0fb8bbf-81b1-45d7-bb27-ac83b5db749e","added_by":"auto","created_at":"2025-11-14 16:07:16","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":252840,"visible":true,"origin":"","legend":"","description":"","filename":"Tables.docx","url":"https://assets-eu.researchsquare.com/files/rs-7983970/v1/2ac5bca79123e75263ba4a87.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Uncorrelated Inequalities: A Multiproxy Measure Suggests Reduced Household Disparity","fulltext":[{"header":"Introduction","content":"\u003cp\u003eInequality has become a popular topic in archaeology. Part of this popularity derives from the conspicuous growth of inequality in contemporary societies (see background section below) and part from the embrace of a measure—the Gini coefficient—that reduces inequality to a single number, conveniently enabling archeologists to use data from various time periods and world regions in the service of cross-cultural comparison and synthesis (Bowles et al., 2010; Fochesato et al., 2019; \u0026nbsp;Kohler et al., 2018; Kohler et al., 2025). In the Maya area, researchers tend to apply the Gini coefficient to architectural variables because extensive data on non-perishable stone buildings can be acquired relatively easily through the use of aerial laser scanning (lidar).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBut looking only at architecture can be problematic. Scholars such as Martha Nussbaum and Amartya Sen (1993) have argued that reducing measures of inequality to a single variable, such as income or monetary wealth, fails to capture a robust view of well-being in any particular society. In what has come to be known as the capabilities approach, well-being derives not just from money but from education, women’s rights, having a voice in governance, and more. Likewise, archaeologists have argued that well-being in the ancient past is also muti-faceted (Arponen et al., 2016; Drennan et al., 2010; Hutson, 2023; Munson and Scholnick, 2022; Twiss et al., 2024). This means that different households within the same society may value (and derive contentment from) different goals; some invest in elaborate houses, others in portable wealth, others in ritual. Thus, we need measures of inequality that embrace multiple variables and accommodate case studies where households that rank highly in some variables rank lower in others.\u003c/p\u003e\n\u003cp\u003eAcquiring robust, multi-proxy evidence for inequality brings three challenges. First, it requires extensive yet costly household excavations. This challenge means that we will have much smaller sample sizes: the number of extensively excavated households per site is low and the number of sites with more than a few such households is small. Ideally, the households in each site’s sample should date to the same time period so that they are part of the same society. To avoid a palimpsest effect that muddies interpretation, households should also have relatively short occupation spans. Since my expertise is in the Maya region, I began this research by compiling Maya case studies. Sites with extensive, well-published excavations in domestic contexts include Uxul, Mayapan, Copan, and Tikal. I also included the southwest Asian settlement of Çatalhöyük because recent research at this site (Hodder, 2022; Kay et al., 2022; Twiss et al., 2024) has closely examined inequality along the lines that I specify below, providing a robust case study that enables comparison from a different part of the world.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe second challenge is that simply calculating Gini coefficients for each variable and averaging them may not lead to an accurate measure of what Oka and coauthors (2018:73) call “general inequality,” particularly in cases where different variables are not correlated. As a hypothetical example, I will continue with the scenario stated above where disparate values lead some households to invest in elaborate houses, others in portable wealth, and others in ritual. Let us imagine that in this example, a settlement’s households each have relatively equal resources (minimal general inequality) but a third of them spend heavily on architecture, another third on personal adornments, and the final third on incense burners. Gini coefficients for each of these three variables (architecture, adornments, and censers) will be high. If, following Oka and coauthors (2018), we treat the average of these three Ginis (the Composite Archaeological Inequality index, or CAI) as a measure for studying trends in equality across societies, the high average Gini for this example cripples the effort to study trends because it misrepresents the fact that households in this settlement have relatively equal resources but expend them in different ways. This instance of misrepresentation merits further discussion as it permits a disambiguation of key terms. Inequality refers to the differential distribution of a valued resource. One can measure inequality for each valued resource (architecture, adornments, censers, etc.). General inequality refers to the degree to which multiple measures of inequality align. When most measures of inequality align, which is to say when some households are poor in most or all ways and others are rich in most or all ways, general inequality is high: resources as a whole are not evenly distributed. Well-being refers to the ability to fulfil desire. Since different people in the same society desire different things (and derive different amounts of happiness from the same quantity of a particular resource), inequality in the distribution of a single resource will not capture well-being (Sen, 1980). However, when general inequality is high, some households experience deprivation in most or even all possible ways, lowering well-being. Thus, well-being has a situational, not absolute, relation to inequality.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo address the second challenge (that averaging Gini scores misrepresents societies where variables for inequality are not strongly correlated), I present the Combined Gini Coefficient (CGC). The CGC takes into account multiple variables and therefore fits the capabilities approach. Yet, unlike measures that average Gini coefficients for multiple variables (e.g. the CAI), the CGC helps distinguish societies in which different forms of inequality correlate with each other (households that score highly on one variable tend to score highly on most others) from societies in which inequalities are not correlated (households that score highly on one variable score less highly on others). Thus, the CGC provides a more accurate picture of general inequality in the past. Oka and coauthors (2018:90) caution that measures that take into account multiple variables for inequality, such as the CAI or the CGC, “cannot be taken as absolute measures of inequality.” Oka and coauthors are definitely correct since poor preservation of ancient lives prevents archaeologists from measuring all possible past inequalities. Yet, to the extent that archaeologists compare inequality from one site or time period to another, whether using a single variable (e.g. Kohler et al. 2025) or multiple variables (e.g. Oka et al., 2018), they are indeed presuming that their preferred measure acts as a “replicable measure of general inequality” (Oka et al., 2018:73). It therefore behooves us to find the most accurate measure possible, even if such a measure is not “absolute.” Further below, I demonstrate how the CGC works using data from the ancient Maya city of Chunchucmil and then apply it to the five case studies with extensive household excavations (Uxul, Mayapan, Copan, Tikal, and Çatalhöyük).\u003c/p\u003e\n\u003cp\u003eThe third challenge is that the ways that people choose to fulfil desires differ from settlement to settlement, making comparison difficult. Meeting this challenge requires measuring as many resources as possible. While no two settlements will have the same proxies for inequality, this does not mean that we will forever be comparing apples to oranges. The resources that people privilege from one society to another may differ, but the patterns in the distribution of resources can be compared. Thus, as long as the variables represent resources that are limited but desired, they can be admitted in a multi-dimensional study of inequality even if the variables are not the same from one settlement to another. The supplementary material provides the reasoning for why each variable used in this study can be understood is worth including as a potential measure of inequality. Given differences in the nature of the data from each site, the absolute numbers of variables per case study are not identical. Yet four of the five case studies with extensive excavations (Tikal being the exception) have either eight or nine variables. The hope is that this relatively consistent number of variables for each settlement will provide robust overall portraits of equality.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe results of the analyses presented further below demonstrate a number of points. First, as predicted by the capabilities approach, different forms of inequality do not always align. In other words, it is not always the case that disparities “travel together, with one form of inequality facilitating or enhancing another” (Twiss et al., 2024:22). Second, the relationship between house size and combined measures of inequality can be unpredictable. These points echo univariate studies of inequality, using much larger samples, that have demonstrated that “different historical paths are empirically evident, and they reveal patterns and trends that are neither uniform nor linear” (Feinman et al., 2025:6). These conclusions are important because a refined measure of general inequality can challenge narratives about the durability of inequality. Researchers find that Gini coefficients for ancient, state-level societies are often similar to Gini coefficients for contemporary societies, thus making fairly high levels of inequality seem historically natural and unavoidable. The results from Uxul, Copan, and Mayapan show that ancient inequality was in fact lower than what we would assume on the basis of univariate Gini coefficients. In other words, high levels of inequality are not natural or unavoidable, a point on which I now elaborate. \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/p\u003e"},{"header":" Background","content":"\u003cp\u003eIncreased academic concern with inequality dates back to the 1990s, when social scientists noticed dramatic increases in wealth disparities (Grusky and Kanbur, 2006). Governments, international organizations, and media paid increased attention by about 2015 when institutions such as the United Nations and the International Monetary Fund recognized inequality as a major threat to sustainable development (Philips, 2020:29-30). Though inequality within developed countries had been on the decline for the first three quarters of the twentieth century, due in part to progressive taxation, destruction of wealth from world wars, and burgeoning state investment in education, healthcare, social security, etc., it has grown sharply since the 1980s (Milanovic, 2016:4, Piketty, 2014, 2021:7-8). Within less-developed countries, globalization has led to explosive growth of inequality over the past four decades (Hung, 2021:7). In 2019, the wealth of the 26 richest people on the planet exceeded that of the poorest 50% of the world’s population combined (Philips, 2020:14). The COVID-19 pandemic exacerbated the situation (Franklin et al., 2020:757).\u003c/p\u003e\n\u003cp\u003eThe uptick in inequality gained attention not because of such gaudy trivia, but because of the deep and multi-faceted harm it causes. Wilkinson and Pickett’s (2009:494) literature review shows strong associations between greater income inequality and poor educational performance, low social capital, and higher rates of suicide, low birth weight, teen pregnancy, mental illness, homicide, violent crime, imprisonment, drug overdose, obesity, hostility, and racism. Nobel Prize Winner Joshep Stiglitz (2012:xii) writes that extreme inequality results in an \"economic system that is less stable and less efficient, with less growth” and fewer opportunities for social mobility (see also Cunha Neves et al., 2016). High inequality imperils democratic governance (Deaton, 2014; Rau and Stokes, 2025) and threatens political stability as it empowers only a small sliver of the society and leaves a “working class suffering from stagnant or declining income” (Hung, 2021:12). \u0026nbsp; High inequality often results in political violence, civil wars, revolutions, financial crises, and social movements. While tumultuous and bloody, such events tend to bring inequality back down (Piketty, 2022:10; Scheidel, 2017).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eOne of the reasons why social scientists take great interest in the topic is that massive inequality is not inevitable. Rather, political ideology affects it (Stiglitz 2012). “Inequality does not follow a deterministic process…There are powerful forces pushing alternately in the direction of rising or shrinking inequality. Which one dominates depends on the institutions and policies that societies choose to adopt” (Piketty and Saez, 2014:841). If inequality is a “social, historical, and political construction” (Piketty, 2022:9), then people can deconstruct it. While generations of anthropologists and archaeologists have clarified that inequality is part of our primate heritage and can be found anywhere, this same body of research confirms that societies have devised creative strategies for constraining inequality (Ames, 2010; Graeber and Wengrow, 2021; Hodder, 2022; Weissner, 2002). As Ben Philips (2020:4) writes, “The problem we face in beating inequality is not that we do not know what needs to be done , it's that we haven't brought together the collective power to overcome those who are stopping it from being done.\" Indeed, cross-cultural comparison suggests that collective action can reduce inequality (Blanton and Fargher, 2008). This finding motivates recent research that attempts to understand the degree to which variation in how people govern themselves affects the amount of inequality in ancient societies is (Carballo and Feinman, 2016; Feinman et al., 2018, 2025 Hutson et al., 2023; Kohler et al., 2018).\u003c/p\u003e\n\u003cp\u003eThis paper contributes to comparative discussions of inequality by developing and applying a new method for quantifying degrees of inequality. Inequality is complex and protean. Different ways of measuring it lead to paradoxical conclusions. For example, one country’s inequality compared to another can diminish at the same time that inequality within that country increases (Hung, 2021; Sen, 2006:21). Poverty can climb drastically even when a country officially moves from “poor” to “middle income\" (Philips, 2020:12). Nobel prize winner Amartya Sen illuminates a number of issues with the measurement of inequality and underscores the importance of using multiple proxies for wealth. In some societies, multiple proxies are closely linked, therefore allowing a single measure to characterize inequality more generally. Yet in other societies, one measure of wealth does not correlate with another. In these cases, we need a new way to characterize overall inequality if we wish to be able to make comparisons. Sen’s work has begun to influence archaeological studies of inequality (Arponen et al., 2016; Munson and Scholnick, 2022; Smith, 2015) and frames the methodological considerations in the following section.\u003c/p\u003e\n\u003cp\u003eAligned and Un-aligned Inequalities\u003c/p\u003e\n\u003cp\u003ePut very simply, in his capabilities approach, Sen (1980) recognizes that using a single measure of inequality, such as income, often fails to capture variation in quality of life for two reasons. First, well-being is multi-faceted, involving basic concerns such as nourishment, clothing, and shelter but also outcomes that income does not directly capture, such as social respect, career fulfillment, political voice, and opportunities for women (Sen, 1993, 2006:35; see also Drydyk, 2005; Nussbaum, 2005; 2006). Second, within any particular society, individual people and groups “differ a good deal from each other in the weights they attach” to particular values and the contentment they derive from income or other physical goods (Sen, 1993:39; Stewart, 2005). If human development is therefore about expanding choices and growing opportunity, then any assessment of the human endeavor requires multiple measurements (Piketty, 2022:22). Sen’s argument helped shape the United Nations Development Programme’s (UNDP) Human Development Reports, which, beginning in 1990, recognized the importance of not just financial wealth, but also a society’s health, human rights, creativity, political freedom, and more (UNDP, 1990). The UNDP created the Human Development Index (HDI) as an explicitly multidimensional measure of the standard of living, combining income, literacy and life expectancy (Grusky and Kanbur, 2006:11).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn archaeology, many studies of inequality focus narrowly on house size (Basri and Lawrence, 2020; Betzenhauser, 2018; Brown et al., 2012; Ellyson et al., 2019; Hutson et al., 2023; Kohler et al., 2025; Squitteri and Altawheel, 2022; Thompson et al., 2021). Focusing on house size has several advantages. Archaeologists in Mesoamerica often observe a correlation between house size and wealth (Folan et al., 2009; Haviland and Moholy-Nagy, 1992; Carmean et al., 2011; Tourtellot et al., 1992). According to Smith and coauthors (2014:312), houses of the rich are larger than houses of the poor for two reasons. “First, larger houses are more costly to construct, using more material, time, and labor, and thus show a positive association with household wealth. Second, wealthier households often construct larger and more elaborate residences to display their wealth or position.” Furthermore, if houses are larger because more people live in them or they have greater storage needs, these concerns also involve inequality since an increase in residents means greater access to labor and more storage means possession of more resources (Kohler et al., 2025). Another advantage of using house size is that it can often be measured without excavation, therefore enabling the collection of large samples at relatively low cost. Finally, house size enables standardized comparisons between sedentary societies across the world and across multiple time periods (Chase et al., 2023; Kohler et al., 2018). Yet focusing on house size alone also has drawbacks. House size does not always correspond with wealth (Hodder, 2016; Hutson, 2016:148-151; Kay et al., 2022:586) and may relate instead to the nature or household activities, previous construction not related to current occupants, the politics of labor organization, formation processes, and more (Hendon, 1992; Kay et al., 2022; Kuijt, 2024; Munson et al., 2023; Oka et al., 2018:71; Peterson and Drennan, 2018:44, 48; Peterson et al., 2016:214; Walden et al., 2023).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMulti-proxy analyses mitigate an over-reliance on house size. They also help distinguish different kinds of inequalities, such as material (tangible resources such as tools and buildings), relational (social and political connections), and embodied (corporeal and intellectual expertise) (Bowles et al., 2010). A sample of recent multiproxy studies in archaeology includes Feinman and colleagues’ (2018) examination of obsidian, bone, house size, patio size, and terrace size in the Valley of Oaxaca, Nishimura’s (2023) exploration of 13 variables, including architecture, artifacts and burials, from Bronze Age Titriş Höyük, Turkey, and Wright’s (2014) and Twiss and collaborators’ (2024) examinations of over a dozen variables at neolithic Çatalhöyük (see also Fochesato et al., 2019; Stone, 2018; Oka et al., 2018).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMultiproxy studies in which patterns from one variable differ from patterns in another variable have the potential to explore the complexity of inequality in the spirit of Sen’s capabilities approach. For example, Munson and Scholnick’s (2022; see also Munson et al., 2023) study of burials at Altar de Sacrificios shows that there was very little inequality in terms of skeletal health, reflecting embodied well-being, but substantial inequality in terms of personal adornments, reflecting material wealth. Proxies for social connectedness fell in between material wealth and embodied well-being. Kohler and Higgins’ (2016) comparison of house size and storage space among ancestral Puebloans suggests to them a distinction between wealth and income. Ortman and colleagues (2025) argue, on the other hand, that house size is a better indicator of income than of wealth. Studies from Çatalhöyük show, among other things, that the houses with the most burials and symbolic elaboration (such as bucrania) are not the houses with the most surface area or the most storage space (Hodder, 2022:623; Kay et al., 2022).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe work of Robert Drennan and Christian Peterson (2006, 2012; Drennan et al., 2010; Peterson and Drennan, 2018; Peterson et al., 2016) provides a sustained engagement with different kinds of inequality and the multiple proxies required to tease these out. At the Hongshan (4500-3000 BCE) site of Fushanzhuang, in the Chifeng region of China, they find two separate but uncorrelated hierarchies: one of wealth—as indicated by finely made and better finished ceramics—and one of status (Drennan et al., 2010:59) or prestige (Peterson et al., 2016:209)—as indicated by decorated pottery. Likewise, at Yuchisi, a Late Dawenkou (3500-2600 BCE) central place in Anhui province, China, personal adornment, which Peterson and coauthors equate with prestige, does not correlate with serving vessels and fine-paste ceramics, which they equate with wealth. On the other hand, during the Guadalupe phase (900-700 BCE) at Fabrica San Jose, a village in the Valley of Oaxaca, “status and wealth are intertwined…and this integrated system of ranking emerges strongly from the household evidence” (Drennan et al., 2010:62). Likewise, at Dadiwan, a large, Late Yangshao period (4000–3000 BCE) settlement in Gansu province, China, households with greater wealth also have greater indicators of status; wealth and status were unified into a single, clear axis (Peterson et al., 2016:206, 210).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe contrast highlighted by Drennan and Peterson—societies where variables for wealth and prestige align versus societies where they do not—also exists in the Maya area. A clear example comes from Tikal and Chunchucmil, a pair of cities which reached similar populations (about 40,000 to 45,000 for Tikal [Haviland, 1970:193, 1972:138, 2003:129]; between 31,000 and 47,000 for Chunchucmil [Hutson et al., 2017]) at approximately the same time (between 550 and 770 CE for Tikal [Haviland, 2003:124-129; 2014:131] and between 400 to 630 CE for Chunchucmil [Jiménez et al., 2017]). Both cities feature central marketplaces (Jones, 2015; Dahlin et al., 2007). At Tikal, house size, access to obsidian, access to seashell, and assemblage diversity and are all positively correlated (Hutson, 2020:72-3). At Chunchucmil, residential floor area, architectural volume, access to obsidian, fancy pottery, and other resources are not correlated (Hutson, 2020:72-3). In line with Sen’s capabilities approach, the lack of correlations at Chunchucmil can be interpreted as a case in which different households had the freedom to pursue different pathways to well-being. Inequalities existed, but they are “domain-specific” (Kay et al., 2022:584) at Chunchucmil. While some households invested more in material wealth, others invested more in social wealth. To quote Munson and Skolnick (2022:4), \"what people value in life (e.g., what they strive ‘to be and do’) differs not only between societies but within them as well.\"\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn cases like Fábrica San José and Tikal, richer households specialize in craft production. Excavations at Early Bronze age III (2850-2550 BCE) Numayra, Jordan, and 7\u003csup\u003eth\u003c/sup\u003e century CE Cerén, El Salvador, specialization leads not to clear differences in well-being among households but rather horizontal differentiation and degrees of interdependency (Oka et al., 2018:87; Sheets, 2020).\u003c/p\u003e\n\u003cp\u003eQuantifying overall inequality when inequality is domain-specific: The Combined Gini Coefficient (CGC)\u003c/p\u003e\n\u003cp\u003eWhereas sites like Fábrica San Jose, Tikal, and Dadiwan exhibit clean, homogeneous hierarchies, the findings at Fushanzhuang, Yuchisi, Chunchucmil, Numayra and Ceren exhibit domain-specific inequalities that are not correlated, akin to “a rich mosaic of varied relationships—cooperative, competitive, or conflictive” (Peterson and Drennan, 2016:220). Inequality among households in the second list of sites is not as pronounced as inequality in the first list of sites. But how do we quantify inequality more generally at sites where inequality is domain-specific; e.g. settlements where different measures of well-being are not correlated?\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAs mentioned in the introduction, Oka and colleagues (2018) propose a generalized measure of inequality that they call the Composite Archaeological Inequality index (CAI). The CAI is the geometric mean of the Gini coefficients of all available variables. By aggregating multiple measures of well-being, the CAI takes inspiration from the HDI, and therefore operates under the logic of Sen’s capabilities approach. Yet in cases like Yuchisi and Chunchucmil, where variables for inequality are not correlated, the CAI overestimates the degree of inequality. For example, if the Gini coefficients for fine pottery, access to exotic trade goods, and volume of domestic architecture are .52, .56, and .60, the CAI/geometric mean (as well as the arithmetic mean) would be .56. But if the households with the most fine pottery do not live in the most voluminous houses and the households with access to abundant trade goods possess relatively little fine pottery, etc., averaging the Gini scores misses the fact that material wealth is broadly dispersed across many households. This dispersion means that overall inequality would be lower than what the CAI suggests.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eDrennan and Peterson (2006) resolve this problem through multi-dimensional scaling, which creates visual representations of how individual households differ from each other along multiple axes of variation. While useful for understanding the rich mosaic of human striving at a particular settlement, multi-dimensional scaling does not enable quantitative comparison of generalized levels of inequality from one settlement to the next.\u003c/p\u003e\n\u003cp\u003eThe method proposed in this paper—the Combined Gini Coefficient, or CGC—allows for such comparison. Like most previous studies, this method uses the domestic compound (understood to be the archaeological remains of a household) as the unit of analysis. Each domestic compound has a value for each variable (house size, access to fancy pottery, etc.) whose distribution can be indicate inequality. For each variable, all variates are converted into scores between 0 and 100, such that the domestic compound with the highest value for a variable receives a 100 for that variable. After converting variates to scores between 0 and 100 for each variable, each domestic compound’s scores are summed and a Gini coefficient is calculated from the sums of scores.\u003c/p\u003e\n\u003cp\u003eI will demonstrate the CGC method using data from six variables measured on 113 domestic compounds at Chunchucmil. The first variable, amount of obsidian, is a potential measure of wealth since obsidian is a long-distance trade good (the nearest source is over 600 km away as the crow flies) that requires resources to acquire. The values for this variable range from 0 to 18.9 grams per kg of pottery. A household with no obsidian would get a score of 0. The household with 18.9 grams of obsidian per kg of pottery—S6W4b (Operation 116)—receives a score of 100. A household with 6.3 grams of obsidian per kg of pottery, which is a third of the way between 0 and 18.9, would receive a score of 33.3. The values for the second variable, the amount of fancy pottery (measured in kg per total kg of pottery), range from 0 to 10.5. Domestic compound S6W4b happens to have no fancy pottery, thus receiving a score of 0. Moving to a third variable, volume of architecture, values range from 15.8 to 5337.6 m\u003csup\u003e3\u003c/sup\u003e, such that 15.8 converts to a score of 0.003 and 5337.6 converts to a score of 100. S6W4b has a volume of 298.6 m\u003csup\u003e3\u003c/sup\u003e, which falls near the low end of the range, and converts to a score of 5.1. Following the same procedure, S6W4b would receive scores for the remaining three variables (surface area of houses, amount of metates, and amount of depressions). S6W4b’s scores for the six variables would then be summed, as would the scores for each of the other 112 domestic compounds. The Combined Gini Coefficient (CGC) for these 113 scores, each of which combines six variables, is 0.357.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis particular Gini score—0.357—is remarkable given that the Gini scores for each of the six variables range from 0.465 to 0.725. The arithmetic mean of these six Gini scores is 0.556, while the geometric mean (Oka and coauthors’ CAI) is 0.550 (see table 1). Thus, the CGC, which is attentive to domain-specific inequalities, shows overall inequality to be substantially lower than when calculated simply by averaging Gini scores. I argue that the CGC is more accurate because, unlike the arithmetic or geometric (CAI) averages of Gini scores, it takes into account cases in which variables for well-being are not correlated with each other: cases where different forms of inequality don’t “travel together” (Twiss et al. 2024). \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFinally, does the CGC allow comparison among different settlements? This question re-iterates the third challenge that I mentioned in the introduction. Even within the same region, artifact assemblages and other resources may differ across time and space such that variables for material well-being may differ from one settlement to the next. Thus, since the CGCs for different sites will contain different sets of variables, it would seem that comparing CGCs commits the error of not comparing like with like (Chase et al., 2023). Yet it would be dangerous to assume that the same variables that index inequality at one settlement necessarily index inequality for all settlements in the comparison. As an example, access to obsidian prismatic blades was unrestricted within Late Classic Copan (Aoyama, 2001; Hendon, 1991:909), with most households producing their own blades (Mallory, 1984). Blade counts should therefore not be used in the portfolio of variables used to measure overall inequality at Copan. At sites located much further from obsidian sources, however, obsidian can be more limited, making it an admissible variable when exploring patterns of inequality. In this paper, many variables pertain to what Bowles and coauthors (2010) would refer to as material wealth. A few could be argued to have a relational aspect in addition to a wealth aspect. For example, the number of sources of exotic shell to which a household had access at Çatalhöyük may index the number of trade partners. Likewise, a few variables have wealth, relational, and embodied aspects: musical instruments and incense burners at Uxul presume performative and/or ritual knowledge and skills learned from others that become embodied in individuals. The strength of the CGC is that it attends to different ways of life but includes as many variables as possible in order to produce a more generalized snapshot of inequality.\u0026nbsp;\u003c/p\u003e"},{"header":"Results: Applying the Combined Gini Coefficient","content":"\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;The shortcoming of the Chunchucmil example in the previous section is that most of the data comes from test pitting. Of the 113 residential groups in the sample, the average surface area of excavation was 7.5 m\u003csup\u003e2\u003c/sup\u003e (this figure does not include the few groups that received horizontal excavations). While Peterson and co-authors (2016:201) maintain that relatively minor excavations can “provide large samples of artifacts for comparative analysis”, other studies show that test pitting, as opposed to broader excavations, can miss important aspects of ancient household organization, production, and consumption (Masson and Peraza Lope, 2014:336). Thus, I want to focus the CGC on case studies with extensive household excavations. The obvious trade-off is that, due to the high cost of extensive broad-scale excavations, the case studies with well-reported household data have relatively small sample sizes of excavated houses. The current study includes ten well excavated house compounds from Uxul, eight from Mayapan, nine from Copan, and 13 from Çatalhöyük. I also include 34 domestic contexts from Tikal; these contexts are not as thoroughly excavated as those at Uxul, Mayapan, and Çatalhöyük, but are better excavated than most contexts at Chunchucmil. Fortunately for archaeologists constrained by the difficulty of conducting broad-scale household excavations, Fochesato and colleagues (2019:865) show that “relatively small samples from much larger populations yield reasonably accurate and precise estimates of the Gini coefficient.”\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Uxul, located in the Central Maya Lowlands of Campeche, Mexico, was a secondary center heavily influenced by enormous Calakmul, located 32 km to the northeast (Grube et al., 2012). While Uxul has occupation dating to the first Millennium BCE, excavations reveal that most of its structures were built and occupied between 650 and 750 CE (Barnard, 2021:57), when it housed several thousand people. Thus, the residential contexts have reasonable chronological control, though the sample is likely not representative of the site as a whole given that no small residential compounds were excavated extensively. Drawing on data published by Barnard (2021), I included nine variables in the analysis: residential surface area, architectural volume, and amounts of obsidian, greenstone, polychrome pottery, shell artifacts, incense burners, figurines, and musical instruments (table 2, Supplementary table 1; see Supplementary Materials for discussions of these variables and those in the rest of the sites below). None of these variables are significantly positively correlated (see table 3). I therefore anticipate a low CGC. Indeed, while the average of the Gini coefficients for these nine variables is 0.496 (CAI is also 0.496), the CGC is 0.238 (table 1; figure 2a, 3). This result agrees with the finding that domestic compounds with substantial architecture at Uxul did not have better access to ceremonial facilities, water sources, and other services (Barnard, 2021:172-173), a finding which contrasts with common patterns (Dennehy et al., 2016; Stanley et al., 2016). If smaller residential compounds were excavated and included in the sample, the CGC would probably be higher, but so would the Gini scores for individual variables.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Mayapan, located in the northern Maya lowlands of Yucatan, Mexico, was the capital of a political confederacy from 1250 CE to 1450 CE and the largest Maya center of its time, reaching a population of about 15,000. Broad-scale excavations of eight domestic compounds show relatively short occupations and the sample of eight is representative in the sense that it includes what the excavators argue to be both elites and commoners, some with craft specialization and some not. Drawing on published data (Masson and Peraza Lope, 2014; Masson et al., 2021), I included nine variables in the analysis: residential surface area and amounts of obsidian, chert, chert points, fancy pottery, imported pottery, ritual pottery, shell artifacts, and metal artifacts (table 4, supplementary table 2). Table 5 shows the 36 correlation coefficients for these variables, of which only three are significantly positive. The average of the Gini coefficients for these nine variables is 0.491 (nearly identical to Uxul’s average), with a CAI of 0.472 (table 1). In contrast, the CGC is 0.155 (figure 2b, 3). This low CGC falls in line with an earlier study suggesting minimal inequality at Mayapan (Brown et al., 2012) and would be expected given the weak correlations between variables.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Çatalhöyük is a densely packed seventh millennium BCE settlement located on the Konya plain in Turkey. Its large number of inhabitants (up to a few thousand), make it anomalous for its time. It lacked features of Old World cities from later time periods, such as centralized political and religious institutions. Hodder (2022) has argued that egalitarian leveling mechanisms constrained aggrandizers who lived in the more elaborate buildings. Twiss and coauthors (2024) present extensive data from three phases at Çatalhöyük. I focus on the Middle Occupation phase (6700-6500 BCE), which has by far the largest sample (n = 13) of extensively excavated houses. I used eight variables, including number of grinding tools, paintings, faunal installations, human burials, grave goods, exotic shells, exotic shell sources and exotic stone beads (table 6, Supplementary table 3). Of the 13 houses, surface area measurements were available for only 11. Thus, although I calculated a Gini for surface area (see table 1), the variable was not included in the calculation of the average Gini scores, the CAI, and the CGC. The average Gini score is 0.592 (CAI is 0.563) with a CGC of 0.447 (figure 2c, 3). The relatively high CGC reflects the fact that 39% (11 of 28) of correlations between variables are significantly positive (see table 7).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Tikal, located in Peten district of Guatemala, is a very large Maya city with regional political clout rivalled only by the Kaan dynasty of Calakmul/Dzibanche. Data come from domestic excavations well-reported by Haviland (2014). As noted above, domestic contexts at Tikal were not as broadly excavated compared to Uxul, Copan, Mayapan, and Çatalhöyük. Furthermore, whereas the domestic occupations at the other sites generally span 200 years or less, many of the domestic compounds at Tikal had much longer occupations, amplifying a palimpsest effect that injects more caveats into the interpretation of inequality. Another potential problem is that Tikal has only half the variables as the other four sites with extensive excavations (composite indices tend to stabilize with more variables: Oka et al., 2018:90). Finally, the excavation sample only includes non-elite domestic compounds (recall that the Uxul sample is biased toward large compounds). Despite these downsides, I include Tikal in the case study because, unlike the other Maya cases, its variables for material well-being are more strongly correlated (see Supplementary table 4). In other words, variables for inequality travel together. We would therefore anticipate a higher CGC. As expected, the CGC for Tikal is 0.481 (table 1, figure 2d), higher than the other CGCs (figure 3), and closer to the average of its Gini scores, 0.598. Such scores would be even higher if the excavation sample contained elite households. Given the other shortcomings of the Tikal case (longer occupation, fewer variables, less extensive excavation), the result for Tikal may not be as trustworthy.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Copan, located in the southern lowlands in western Honduras, is one of the best-known Maya sites. It was a city state capital with a peak population of 20,000 people and an extensive corpus of hieroglyphic inscriptions centered on a dynasty with at least 16 consecutive kings. Copan benefits from several projects focused on household archaeology (for example Landau, 2016; Webster and Gonlin, 1988). I use data from the Proyecto Arqueológico Copan II, directed by William Sanders from 1981 to 1985, because it featured complete and well-published excavations of households from all four status ranks, all within the city and all dated to the Late Classic Coner Phase (650-820 CE). The sample consists of nine patio groups (see Supplementary table 5). While some of these groups are part of larger architectural compounds, such as 9N-8, the “repeated occurrence” of basic household activities at each patio group “suggests that each patio functioned as a separate social-residential unit” (Hendon, 1991:904; see also Hendon, 1987: 488-489; Abrams, 1994). I used nine variables: residential surface area, architectural labor investment, extent of sculpture, imported fancy pottery, quantity of portable ornaments, figurines, bifacial projectile points, worked bone and proportion of basalt grinding stones/metates (table 8). I expected these variables to be correlated given that Fash (2005:96) notes that the “quality of the architecture, graves and tombs, and associated domestic artifacts generally correspond quite well” with the size of domestic compounds at Copan (see also Richards-Risetto, 2023). However, beyond the well-known, strongly positive correlations between architectural labor investment and residential surface area, and architectural labor investment and sculpture, only four of the remaining 34 potential correlations were statistically significant (table 9), and these remaining correlations are not intuitive (for example, number of figurines and bifacial points). Given the general lack of alignment between variables, the CGC was significantly lower than the average of the Gini scores for the nine variables (Table 1, Figure 3).\u003c/p\u003e"},{"header":"Discussion and Conclusions","content":"\u003cp\u003eWhen put into broader context, the CGCs for the five sites with extensive household excavations reveal a number of points about inequality. The first point is the different ways that inequality manifests itself. Figure 3 shows this clearly. The arithmetic average for the Gini scores of the variables for all sites are somewhat similar, ranging from 0.422 to 0.598. Yet this apparent similarity conceals the fact that in cases like Uxul, Copan, and Mayapan, the full range of resources are much more equitably distributed, as revealed by the relatively low CGCs. In other words, due to weak correlations among variables at Mayapan, Copan, and Uxul, households with a lower-than-average house surface area, for example, do not necessarily have lower-than-average shares of fancy pottery. In this way, variation in one resource counteracts variation in another measure, evening out and dampening overall inequality. On the other hand, at Tikal, patterns in one measure corroborate patterns in other measures, thus amplifying inequality across the board; households that score highly for one measure tend to score highly in other measures. Yet, as discussed above, aspects with the Tikal data set undercut confidence in the results for this site.\u003c/p\u003e\n\u003cp\u003eRegarding Copan, Uxul and Mayapan, one might wonder how it can be that variables tied to material resources show no correlation. A straightforward explanation is that people have similar amounts of resources but choose to invest them in different pursuits. For example, if it takes wealth both to build a larger house and to acquire fancy pottery, these two variables can be uncorrelated if some households choose to invest resources in architecture and others choose to invest resources in pottery. Following Amartya Sen (1980) and Ted Fischer (2014), there might be multiple ways to find fulfilment within a particular society. Different people might value different pursuits, resulting in a lack of correlation. In such a case when variables for inequality do not travel together and the CGC is lower, general inequality is also lower, meaning that well-being is more broadly distributed. When general inequality is greater, many people will have very few resources to begin with, while others will have lots of resources. In this situation, reminiscent of Tikal, variables for different resources are more likely to be correlated and larger proportions of the population would have lower levels of well-being.\u003c/p\u003e\n\u003cp\u003eInsofar as the CGC suggests a generalized picture of well-being and inequality, the results show a continuum between lower and higher overall inequality (figure 4). The results also show that surface area of architecture does not help predict overall inequality. Figure 3 shows that, among the Maya sites, the CGCs range widely but the Ginis for surface area are nearly identical, with the exception of Copan. In this small sample, surface area Ginis tend to over-represent inequality. Expanding the sample of surface area Gini coefficients to the 15 sites reported by Chase and coauthors (2023) shows that domestic surface area in the Maya area varies substantially, from 0.32 to 0.7, with an average of 0.46 (Figure 4). This average is similar to the average Gini for house surface area for 155 sites in Mesoamerica more broadly (Figure 4; Kohler et al. 2025).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFor Çatalhöyük, the domestic surface area Gini under-represents inequality. Though Çatalhöyük has been described as an egalitarian settlement that lacks some of the features of later settlements that are unquestionably urban, its CGC is in fact higher than cities like Uxul, Copan, and Mayapan. Thus, different measures of inequality traveled together at Çatalhöyük to a greater degree than at the Maya sites. While fine-grained analyses at Çatalhöyük “suggest a society grappling with the tensions between maintaining egalitarian norms and evolving social complexities” (Twiss et al., 2024:25; see also Wright, 2014), the CGC comparisons suggest Çatalhöyük may have been less egalitarian than some of the urban, politically centralized Maya settlements in this study. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAlternatively, one might argue that the CGCs are misleading because each variable has the same weight. This critique is understandable for Copan where a variable such as architectural labor investment should probably be given more weight other variables. For example the resources used to build patio 9N-8a likely exceeded the resources needed to acquire a large proportion of basalt metates or bone ornaments, yet these two variables carry the same weight.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Figure 4 places the CGCs in a more recent and global context of capital ownership. The intensive agriculturalist Gini of 0.57 reported by Shenk and coauthors (2010) represents an average of land and livestock Gini coefficients from four historic societies: East Anglians, Kipsigis, Krummhörn, and Yomut. The three recent Ginis for capital ownership in Scandinavia (0.58), Europe (0.67) and the United States (0.73) are taken from data presented by Piketty (2014). Though capital ownership captures wealth inequality more accurately than measures of inequality based on income from labor, it suffers from the shortcoming of all single proxy measures: many other factors beyond capital (freedom of artistic and political expression, availability of education, etc.) contribute to well-being. Nevertheless, it is notable that these Ginis are higher (often beyond the 95% confidence interval) than the CGCs from some of the ancient societies in this study. This is important because studies that largely limit samples of “preindustrial” societies to the 18\u003csup\u003eth\u003c/sup\u003e and 19\u003csup\u003eth\u003c/sup\u003e centuries risk drawing the oversimplified conclusion that “income inequality in pre-industrial countries today is not very different from inequality in distant pre-industrial times” (Milanovic et al., 2011:268). Once again, contemporary analysts can learn from ancient societies.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; Taken together, the data from Figure 3 suggest that inequality of material well-being as represented by the CGCs in some ancient Maya societies is over-estimated by existing Gini measures while the data in Figure 4 suggest that inequality in some ancient Maya societies was significantly lower than in other societies. Admittedly, Uxul’s CGC would be higher if the excavation sample included more small houses and Tikal’s CGC would be higher if the sample included more large houses. Nevertheless, the results and comparisons presented in this paper underscore the need for a method for disambiguating societies in which variables for well-being are correlated from societies in which they are not. The CGC provides this method while also suggesting the existence of relatively low levels of inequality even in urban, state-level societies. In the context of research that shows the devastating effects of growing inequality, this latter finding adds yet another voice challenging the notion that high inequality is inevitable. While the small sample sizes in this paper demand humility and caution, the hope is that the paper will stimulate methodological experimentation in other multi-proxy data-sets from broadly excavated domestic contexts.\u003c/p\u003e"},{"header":"Statements and Declarations","content":"\u003cp\u003eThe author has no competing interests to declare.\u003c/p\u003e\n\u003cp\u003eNo funding was received for conducting this study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplementary materials\u003c/strong\u003e\u003cstrong\u003e:\u0026nbsp;\u003c/strong\u003eRationale for variable selection and presentation of household data\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement:\u003c/strong\u003e Data used in this paper derive from previously published sources.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAbrams, E. (1994). \u003cem\u003eHow the Maya built their world\u003c/em\u003e. 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Households, corporate groups and food processing tools at neolithic \u0026Ccedil;atalh\u0026ouml;y\u0026uuml;k. \u003cem\u003eJournal of Anthropological Archaeology\u003c/em\u003e 33, 1-33.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTables 1 to 9 are available in the Supplementary Files section\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-archaeological-method-and-theory","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jarm","sideBox":"Learn more about [Journal of Archaeological Method and Theory](http://link.springer.com/journal/10816)","snPcode":"10816","submissionUrl":"https://submission.nature.com/new-submission/10816/3","title":"Journal of Archaeological Method and Theory","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Inequality, households, Gini coefficient, Maya","lastPublishedDoi":"10.21203/rs.3.rs-7983970/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7983970/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eExtreme inequality has received increased attention in the social sciences since the 1990s, in part because of the harm it causes and in part because it is avoidable. Bolstered by the Gini coefficient, a quantitative measure of inequality that enhances comparative studies across time and space, archaeologists have expanded the study of inequality in recent years. While many studies of inequality in archaeology focus on architecture, multiproxy studies that operationalize a capabilities approach have gained popularity. A challenge of multi-proxy studies is that simply averaging Gini coefficients for multiple variables can misrepresent inequality in societies where variables for inequality are not correlated. This paper introduces the Combined Gini Coefficient (CGC) and applies it to a sample of archaeological case studies with extensive domestic excavations. The CGC helps disambiguate societies where variables for material wealth are aligned from societies where such variables are not aligned. In these latter societies, inequality is lower than estimates based on single or averaged variables. This finding is valuable when set within a broader comparative context because it shows that high inequality seen today is not natural and that ancient case studies are relevant.\u003c/p\u003e","manuscriptTitle":"Uncorrelated Inequalities: A Multiproxy Measure Suggests Reduced Household Disparity","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-14 16:07:11","doi":"10.21203/rs.3.rs-7983970/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-01-23T21:46:59+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-19T03:53:02+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-08T11:09:17+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-07T19:11:50+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"254109270032619802538982525214131841847","date":"2025-11-09T16:43:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"209122204539645281891207459868190716439","date":"2025-11-05T09:52:40+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"310241856216767091616930109524787253347","date":"2025-11-05T09:16:57+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-04T18:58:17+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-04T18:43:25+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-30T04:40:51+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Archaeological Method and Theory","date":"2025-10-30T01:32:15+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-archaeological-method-and-theory","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jarm","sideBox":"Learn more about [Journal of Archaeological Method and Theory](http://link.springer.com/journal/10816)","snPcode":"10816","submissionUrl":"https://submission.nature.com/new-submission/10816/3","title":"Journal of Archaeological Method and Theory","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"cc325338-47c3-4b27-9312-062f5ff42b43","owner":[],"postedDate":"November 14th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-18T13:09:43+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-14 16:07:11","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7983970","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7983970","identity":"rs-7983970","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}