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

First order stochastic dominance is a core principle of rational decision making. Given two lotteries, A and B, if the probability of winning x or more in lottery A is greater than or equal to the same probability in lottery B for all x, and is strictly greater for at least one x, the decision maker should always prefer lottery A over lottery B. Violations of stochastic dominance can be induced and reversed by coalescing and splitting lottery branches in certain cases. In expected utility theory (EUT) and cumulative prospect theory (CPT), gambles are represented as probability distributions, and thus coalescing and coalescing are obeyed. In the transfer of attention exchange (TAX) model, gambles are represented as branches having probabilities and outcomes, so particular pairs of gambles that will violate stochastic dominance can be constructed. We sought to train people in order to reduce violations of stochastic dominance. We find that, despite compelling training in splitting and coalescing lottery branches, the rate of violations of stochastic dominance was not much affected by training—they are surprisingly robust. People don’t coalesce spontaneously, and training to coalesce, had smaller effects than some of us anticipated.