Probabilities of choices among very similar objects: An experiment to decide between two models

If a person who is offered a choice between a cup of tea and a cup of coffee on several occasions chooses tea more often, we can say that he prefers tea to coffee. Suppose this person is approached with a tray on which he sees one cup of tea and two cups of coffee. Is it conceivable that in several such situations he will choose a cup of coffee more frequently than a cup of tea? We feel not. Yet a reasonable model of probabilistically defined preference implies that he might do just that (roughly because if his choices were entirely random, the probability of choosing coffee in the 3-cup offer would be twice that of choosing tea). This somewhat paradoxical conclusion is put to a test in an experiment where “wagers,” for which the subjects are assumed to have different (probabilistically defined) preferences, take the place of cups with tea and coffee.