On Locally Rationalizable Social Choice Functions

Abstract

We consider a notion of rationalizability, where the rationalizing relation may depend on the set of feasible alternatives. More precisely, we say that a choice function is locally rationalizable if it is rationalized by a family of rationalizing relations such that a strict preference between two alternatives in some feasible set is preserved when removing other alternatives. Tyson (2008) has shown that a choice function is locally rationalizable if and only if it satisfies Sen's . We expand the theory of local rationalizability by proposing a natural strengthening of that precisely characterizes local rationalizability via PIP-transitive relations and by introducing the -hull of a choice function as its finest coarsening that satisfies . Local rationalizability permits a unified perspective on social choice functions that satisfy , including classic ones such as the top cycle and the uncovered set as well as new ones such as two-stage majoritarian choice and split cycle. We give simple axiomatic characterizations of some of these using local rationalizability and propose systematic procedures to define social choice functions that satisfy .

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