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Contraction consistent aggregation on trees

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  • Mihir Bhattacharya

    (Ashoka University)

Abstract

We study contraction consistent social choice functions (s.c.f.) in a setting where voters have single-peaked preferences over a tree. This is relevant in settings where alternatives are locations spread out on a tree and a location needs to be selected for provision of a public good. An s.c.f. is contraction consistent if its outcome at any profile does not change when the profile is restricted to any subset consisting of the outcome. We show that q-threshold rules on trees} are the only s.c.f.s which satisfy contraction consistency, unanimity and anonymity. These s.c.f.s specify, for each alternative, thresholds which are decreasing (increasing) on every path from a given node. These s.c.f.s then select from the range, the unique alternative which is the smallest (greatest) alternative in any restricted vote profile that receives more additive votes than the threshold assigned to it. These s.c.f.s are generalizations of min, max, and median s.c.f.s when restricted to paths.

Suggested Citation

  • Mihir Bhattacharya, 2023. "Contraction consistent aggregation on trees," Working Papers 96, Ashoka University, Department of Economics, revised 09 Aug 2023.
    • Handle: RePEc:ash:wpaper:96
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    File URL: https://dp.ashoka.edu.in/ash/wpaper/paper96_0.pdf
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    References listed on IDEAS

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    1. Arkarup Basu Mallik & Mihir Bhattacharya, 2025. "Consistency and social choice," Working Papers 142, Ashoka University, Department of Economics.

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