The disjunction effect does not violate the Law of Total Probability

The disjunction effect (DE) refers to an empirical violation of the Sure-Thing Principle (STP), which states that if a person is willing to take an action independently of the outcome of some event, then they must be willing to do so even when the outcome of the event is unknown. A standard practice for inferring a DE, especially in between-subjects experiments, consists of showing a population-level version of this phenomenon, specifically that fewer people are willing to take the proposed action when the outcome of the event is unknown than for any possible known outcome. Although this does not prove a violation of the STP, this population-level condition has received a lot of attention, because it presumably violates the Law of Total Probability, and it is sometimes used as the definition of the DE itself. Here we show that this condition is in fact unrelated to the Law of Total Probability and thus entirely irrelevant for the study of the DE and decision making in general. This calls for a reevaluation of experimental results that have been interpreted as showing a DE based on the above condition. We derive a new disjunction law that can be used to check for violations of the STP in between-subjects data.