Mathematical structure of voting paradoxes. II: Positional voting
type: Item
instance of: scholarly article
title: Mathematical structure of voting paradoxes. II: Positional voting
zbMATH Open document ID: 1081.91007
author: Donald G. Saari
published in: Economic Theory
publication date: 2000-06-22T00:00:00Z
review text: This paper is a companion to the paper immediately preceding it in the journal [Mathematical structure of voting paradoxes. I: Pairwise votes. Econ. Theory 15, No. 1, 1--53 (2000; Zbl 1080.91022)]. In the first paper, the author divided voting methods into positional, where the aggregation rule utilizes how each voter positions, or ranks, the various alternatives, and pairwise methods, where the rule considers majority votes among pairs of alternatives. In the earlier paper, the author primarily studied pairwise systems in comparison to the base case positional system of Borda count. Among many interesting results, he showed that the differences between the methods, and the paradoxes that arise in pairwise methods are due to certain `Condorcet effects'. Positional systems are not subject to these Condorcet effects, but can still differ in their rankings from a given profile. Here, the author analyzes these discrepancies among positional systems. The author utilizes the same profile coordinate system as in the previous paper. Central to his analysis is a concern with rankings of subsets of alternatives, that is, with Independence of Irrelevant Alternatives effects. This focus allows him to show the tremendous variety of plurality rankings that can occur, in fact, all possible combinations of rankings have supporting profiles. The core of the paper involves constructing a theory that explains how such behavior takes place. The author defines a suitable subspace that generates these effects. He shows that Borda count is the unique method that avoids profile deviation effects and that the problems besetting other positional systems are essentially due to a failure to recognize certain symmetries. The paper contains a wealth of interesting new results. The results are clearly explained and their significance brought out. There are numerous examples to illustrate the key points.
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 91B16
zbMATH DE Number: 1415616
zbMATH Keywords: positional voting
zbMATH Keywords: pairwise voting
zbMATH Keywords: voting paradoxes
zbMATH Keywords: social choice
zbMATH Keywords: basic profiles.
reviewed by: Duncan J. Melville
MaRDI profile type: Publication
full work available at URL: s001990050002
OpenAlex ID: W3122331923
Wikidata QID: Q56553626
DOI: 10.1007/S001990050002
description: scientific article; zbMATH DE number 1415616