A unified theory of discrete and continuous responding

Understanding the cognitive processes underlying choice requires theories that can disentangle the representation of stimuli from the processes that map these representations onto observed responses. We develop a dynamic theory of how stimuli are mapped onto discrete (choice) and onto continuous response scales. It proposes that the mapping from a stimulus to an internal representation and then to an evidence accumulation process is accomplished using multiple reference points or "anchors''. Evidence is accumulated until a threshold amount for a particular response is obtained, with the relative balance of support for each anchor at that time determining the response. We tested this Multiple Anchored Accumulation Theory (MAAT) using the results of two experiments requiring discrete or continuous responses to line length and color stimuli. We manipulated the number of options for discrete responses, the number of different stimuli, and the similarity amongst them, and compared the outcomes to continuous response conditions. We show that MAAT accounts for several key phenomena: more accurate, faster, and more skewed distributions of responses near the ends of a response scale; lower accuracy and slower responses as the number of discrete choice options increases; and longer response times and lower accuracy when alternative responses are more similar to the target response. Our empirical and modeling results suggest that discrete and continuous response tasks can share a common evidence representation, and that the decision process is sensitive to the perceived similarity among the response options.