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Voting Procedures for Electing a Single Candidate

Proving Their (In)Vulnerability to Various Voting Paradoxes

verfasst von: Prof. Dr. Dan S. Felsenthal, Prof. Dr. Hannu Nurmi

Verlag: Springer International Publishing

Buchreihe : SpringerBriefs in Economics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book deals with 18 voting procedures used or proposed for use in elections resulting in the choice of a single winner. These procedures are evaluated in terms of their ability to avoid paradoxical outcomes. Together with a companion volume by the same authors, Monotonicity Failures Afflicting Procedures for Electing a Single Candidate, published by Springer in 2017, this book aims at giving a comprehensive overview of the most important advantages and disadvantages of procedures thereby assisting decision makers in the choice of a voting procedure that would best suit their purposes.

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Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

Voting is a common way to resolve disagreements regarding policies to be adopted or candidates to be chosen for various positions and is therefore a necessary ingredient of democratic government. Yet there are numerous voting rules that differ from each other in processing the ballots into voting results. In other words, it is possible that for a given set of voters having a fixed distribution of preferences among the competing alternatives, one would obtain the election of a different alternative as a result of using a different voting rule. We focus on the most obvious desiderata associated with voting procedures, viz., the avoidance of paradoxical outcomes.

Dan S. Felsenthal, Hannu Nurmi

Chapter 2. Voting Paradoxes

Abstract

Voting paradoxes pertaining to the election of a single winner are introduced. The paradoxes are divided into five simple paradoxes and eight conditional ones. The simple paradoxes are paradoxes where the relevant data lead to a ‘surprising’ and arguably undesirable outcome, whereas the conditional paradoxes are ones where the change in one relevant datum while holding constant the other relevant data leads to a ‘surprising’ and arguably undesirable outcome.

Dan S. Felsenthal, Hannu Nurmi

Chapter 3. Voting Procedures Designed to Elect a Single Candidate

Abstract

18 voting procedures for electing a single candidate are introduced and briefly commented upon. The procedures fall into three classes in terms of the type of voter input and Condorcet consistency: non–ranked procedures, ranked procedures that are not Condorcet–consistent and ranked ones that are Condorcet–consistent. The first class consists of four procedures, the second consists of six procedures and the third class consists of eight procedures.

Dan S. Felsenthal, Hannu Nurmi

Chapter 4. The (In)Vulnerability of Non-Ranked Voting Procedures to Various Paradoxes

Abstract

Focusing on four procedures that do not require the voters to submit full preference rankings over candidates (Plurality Voting, Plurality with Runoff, Approval Voting, and Successive Elimination), we discuss, for each procedure, those voting paradoxes to which the procedures are immune and the reasons for this, as well as demonstrate, with the aid of illustrative examples, their vulnerability to other paradoxes.

Dan S. Felsenthal, Hannu Nurmi

Chapter 5. The (In)Vulnerability of Ranked Voting Procedures that Are Not Condorcet–Consistent to Various Paradoxes

Abstract

The (in)vulnerability of six ranked voting procedures which are not Condorcet–consistent (Borda count, Alternative vote, Coombs’ procedure, Bucklin’s procedure, Range Voting and Majority Judgment) to 13 paradoxes is examined in this chapter. For those systems that are vulnerable to some voting paradoxes the vulnerability is demonstrated through illustrative examples showing that there are profiles where the paradoxes in question happen when the respective procedures are in use. And for those systems that are invulnerable to some voting paradoxes the invulnerability is explained.

Dan S. Felsenthal, Hannu Nurmi

Chapter 6. The (In)Vulnerability of the Ranked Condorcet–Consistent Procedures to Various Paradoxes

Abstract

We study the vulnerability or invulnerability of eight voting procedures (Minimax, Dodgson’s, Nanson’s, Copeland’s, Black’s, Kemeny’s, Schwartz’s and Young’s procedures) to 13 voting paradoxes. The invulnerabilities are explained and the vulnerabilities demonstrated through illustrative profiles where the paradoxes occur under the procedures examined.

Dan S. Felsenthal, Hannu Nurmi

Chapter 7. Summary

Abstract

We discuss the findings of the preceding chapters aiming at an overall judgement of the relative merits of the 18 procedures in the light of their (in)vulnerability to various voting paradoxes. No procedure is invulnerable to all the analyzed voting paradoxes, but there are differences in the variety of paradoxes that various procedures are vulnerable to. It turns out that for those emphasizing that a Condorcet Winner ought to be elected when s/he exists, the most plausible voting procedures are associated with the names of Copeland and Kemeny, while for those stressing the need to preserve the basic rationale of voting, viz., the participation condition, the most appealing system is the Borda count.

Dan S. Felsenthal, Hannu Nurmi

Titel: Voting Procedures for Electing a Single Candidate
verfasst von: Prof. Dr. Dan S. Felsenthal
Prof. Dr. Hannu Nurmi
Copyright-Jahr: 2018
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-74033-1
Print ISBN: 978-3-319-74032-4
DOI: https://doi.org/10.1007/978-3-319-74033-1

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