On accessibility of the core in mutidimensional spatial majority voting situations

2026-09-09

AI Summary

本文研究了多维空间多数投票情境下核心的可达性问题，通过分析具有偶数选民的情况，并证明了从任意政策出发，经过有限次多数主导可以达到核心中的政策。

Abstract

In this paper we consider situations of (multidimensional) spatial majority voting. We analyze such situations having an even number (greater than or equal to 4) of voters and assume that each voter's preference over the set of policies is ``Euclidean": i.e., each voter has a most preferred ``ideal" policy and the voter's pay-offs from policies decrease as the (Euclidean) distance of the policies from the ideal policy goes up. We confine attention to voting situations for which the core has a single element belonging to the interior of the policy set. It is known that under conditions usual in this literature, this element of the core, generally, is not a Condorcet winner: i.e., there is at least one policy outside the core such that the core-policy cannot be reached from it by just one round of majority domination. We demonstrate that, however, under such conditions, starting from any policy in place, by a finite sequence of majority-dominations (we assume, implicitly, sincere voting) the policy in the core is reached eventually.

Problem

• multidimensional spatial majority voting
• core
• Condorcet winner
• majority-dominations

Innovation

• multidimensional spatial majority voting
• core policy
• Condorcet winner
• majority-dominations