On Locally Rationalizable Social Choice Functions Article Swipe

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YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2204.05062

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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Rationalizability Axiom Choice function Mathematical economics Mathematics Transitive relation Function (biology) Social choice theory Set (abstract data type) Consistency (knowledge bases) Pure mathematics Computer science Combinatorics Discrete mathematics Nash equilibrium Evolutionary biology Programming language Biology Geometry

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2204.05062
PDF: https://arxiv.org/pdf/2204.05062
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Related Works: 10
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DOI: https://doi.org/10.48550/arxiv.2204.05062

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Title: On Locally Rationalizable Social Choice Functions

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Language: en

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Publication year: 2022

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Publication date: 2022-04-11

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Authors: Felix Brandt, Chris Dong

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Landing page: https://arxiv.org/abs/2204.05062

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Concepts: Rationalizability, Axiom, Choice function, Mathematical economics, Mathematics, Transitive relation, Function (biology), Social choice theory, Set (abstract data type), Consistency (knowledge bases), Pure mathematics, Computer science, Combinatorics, Discrete mathematics, Nash equilibrium, Evolutionary biology, Programming language, Biology, Geometry

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