On the gap between outcomes of voting rules

Mathur, A and Bhattacharyya, A (2017) On the gap between outcomes of voting rules. In: 16th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2017, 8 - 12 May 2017, Sao paulo, pp. 1631-1633.

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Abstract

Various voting rules (or social choice procedures) have been proposed to select a winner from the preferences of an entire population: Plurality, veto, Borda, Minimax, Copeland, etc. Although in theory, these rules may yield drastically different outcomes, for real-world datasets, behavioral social choice analyses have found that the rules are often in perfect agreement with each other! This work attempts to give a mathematical explanation of this phenomenon. We quantify the gap between the outcomes of two voting rules by the pairwise margin between their winners. We show that for many common voting rules, the gap between them can be almost as large as 1 when the votes are unrestricted. As a counter, we study the behavior of voting rules when the vote distribution is a uniform mixture of a small number of multinomial logit distributions. This scenario corresponds to a population consisting of a small number of groups, each voting according to a latent preference ranking. We show that for any such voting profile on g groups, at least l/2j fraction of the population prefers the winner of a Borda election to any other candidate.

Item Type:	Conference Paper
Publication:	Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
Publisher:	International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
Additional Information:	The copyright for this article belongs to International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
Keywords:	Multi agent systems; Probability distributions, Generative model; Latent models; Multinomial Logit; Preference ranking; Real-world datasets; Social choice; Uniform mixtures; Voting, Autonomous agents
Department/Centre:	Division of Interdisciplinary Sciences > Computational and Data Sciences
Date Deposited:	25 Jul 2022 08:42
Last Modified:	25 Jul 2022 08:42
URI:	https://eprints.iisc.ac.in/id/eprint/74686

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