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arXiv · 2204.05062

On Locally Rationalizable Social Choice Functions

Felix Brandt·Chris Dong
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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 $γ$. We expand the theory of local rationalizability by proposing a natural strengthening of $γ$ that precisely characterizes local rationalizability via PIP-transitive relations and by introducing the $γ$-hull of a choice function as its finest coarsening that satisfies $γ$. Local rationalizability permits a unified perspective on social choice functions that satisfy $γ$, 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 $γ$.

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Felix Brandt, Chris Dong. 2024-03-04. On Locally Rationalizable Social Choice Functions. https://arxiv.org/abs/2204.05062

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