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<p>We study <i>contraction consistent</i> 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 <i>contraction consistent</i> if its outcome at any profile does not change when the profile is restricted to any subset consisting of the outcome. We show that <i>q</i>-<i>threshold rules on trees</i> are the only s.c.f.s which satisfy <i>contraction consistency</i>, <i>unanimity</i> and <i>anonymity</i>. 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 cumulative votes than the threshold assigned to it. These s.c.f.s are generalizations of <i>min</i>, <i>max</i>, and <i>median</i> s.c.f.s when restricted to paths.</p>

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Contraction consistent aggregation on trees

  • 期刊论文

  • 发表日期：

    2025年5月21日

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  • Mihir Bhattacharya

摘要

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 cumulative 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.