chapter  6
Domain Conditions for Quasi-transitive Rationalisability
ByDebabrata Pal
Pages 14

In the literature of choice theory an important problem that has been dealt with at length is the rationalisability of choice functions. The problem investigates whether it is possible to conceive of a preference relation that would represent the choice pattern of an individual. If it is observed that an individual chooses x from {x, y}, {x, z}, {x, y, z} and y from {z, y}, it is immediate that the preference relation xRx, yRy, xPy, xPz, yPz1

represents such choice behaviour. The best element (x)2 in the sets {x, y}, {x, z}, {x, y, z} according to the aforesaid preference relation is the same as the chosen element in the sets. Similarly, y is the best as well as the chosen element in the set {z, y}. We, therefore, say that such a choice function3 is rationalisable. In other words, a choice function is rationalisable if and only if the most preferred elements according to some preference relation are chosen from the available sets.