On Locally Rationalizable Social Choice Functions
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909127464189952 |
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| author | Brandt, Felix Dong, Chris |
| author_facet | Brandt, Felix Dong, Chris |
| contents | 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 $γ$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2204_05062 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Locally Rationalizable Social Choice Functions Brandt, Felix Dong, Chris Theoretical Economics 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 $γ$. |
| title | On Locally Rationalizable Social Choice Functions |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2204.05062 |