Surprisingly Robust Violations of Stochastic Dominance Despite Splitting Training A Quasi-Adversarial Collaboration

First-order stochastic dominance is a core principle in rational decision-making. If lottery A has a higher or equal chance of winning an amount x or more compared to lottery B for all x, and a strictly higher chance for at least one x, then A should be preferred over B. Previous research suggests that violations of this principle may result from failures in recognizing coalescing equivalence. In Expected Utility Theory (EUT) and Cumulative Prospect Theory (CPT), gambles are represented as probability distributions, where probabilities of equivalent events can be combined, ensuring stochastic dominance. In contrast, the Transfer of Attention Exchange (TAX) model represents gambles as trees with branches for each probability and outcome, making it possible for coalescing and stochastic dominance violations to occur. We conducted two experiments designed to train participants in identifying dominance by splitting coalesced gambles. By toggling between displays of coalesced and split forms of the same choice problem, participants were instructed to recognize stochastic dominance. Despite this training, violations of stochastic dominance were only minimally reduced, as if people find it difficult---or even resist---shifting from a trees-with-branches representation (as in the TAX model) to a cognitive recognition of the equivalence among different representations of the same choice problem.