Optimal behaviour can violate the principle of regularity

Understanding decisions is a fundamental aim of behavioural ecology, psychology and economics. The regularity axiom of utility theory holds that a preference between options should be maintained when other options are made available. Empirical studies have shown that animals violate regularity but this has not been understood from a theoretical perspective, such decisions have therefore been labelled as irrational. Here, I use models of state-dependent behaviour to demonstrate that choices can violate regularity even when behavioural strategies are optimal. I also show that the range of conditions over which regularity should be violated can be larger when options do not always persist into the future. Consequently, utility theory—based on axioms, including transitivity, regularity and the independence of irrelevant alternatives—is undermined, because even alternatives that are never chosen by an animal (in its current state) can be relevant to a decision.