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Voting Procedures Under a Restricted Domain: An Examination of the (in)Vulnerability of 20 Voting Procedures to Five Main Paradoxes
Cham, Switzerland: Springer Verlag (2019)
Abstract
This book deals with 20 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 five important paradoxes in a restricted domain, viz., when a Condorcet winner exists and is elected in the initial profile. Together with the two companion volumes by the same authors, published by Springer in 2017 and 2018, this book aims at giving a comprehensive overview of the most important advantages and disadvantages of voting procedures thereby assisting decision makers in the choice of a voting procedure that would best suit their purposes.Author's Profile
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Chapters
Summary
This chapter concludes the analysis of the 20 voting procedures in terms of 5 voting paradoxes in restricted domains characterized by the existence of a Condorcet winner which at the same time is elected by the procedure under investigation. The restricted domain provides a perspective to how much d... see more
The Vulnerability of 20 Voting Procedures to the Preference Inversion Paradox in a Restricted Domain
Responsiveness to electoral opinions is one of the hallmarks of democratic governance. We focus on a particularly strong type of unresponsiveness, viz., one where the complete inversion of all preferences in the electorate is accompanied with no change in the electoral outcome. It is known that the ... see more
Which of 20 Voting Procedures Satisfy or Violate the Subset Choice Condition in a Restricted Domain?
The relative desirability of a voting procedure is assessed, inter alia, by verifying which axioms, or postulates, it satisfies or violates. One of these axioms is the subset choice condition . This axiom requires that if a candidate, x, is elected under a given voting procedure, f, in a profile con... see more
The Vulnerability of 20 Voting Procedures to the No-Show Paradox in a Restricted Domain
The No-Show paradox occurs whenever a group of identically-minded voters is better off abstaining than by voting according to its preferences. Moulin’s result states that if one wants to exclude the possibility of the No-Show paradox, one has to resort to procedures that do not necessarily elect the... see more
The Vulnerability of 20 Voting Procedures to the Inconsistency Paradox in a Restricted Domain
This chapter focuses on the possibility that some well-known voting procedures are vulnerable to the Inconsistency paradox even in preference profiles that are characterized by a restricted domain where a Condorcet winner exists and is elected in each disjoint subset of voters but not in their union... see more
The Vulnerability of 20 Voting Procedures to Lack of Monotonicity in a Restricted Domain
This chapter focuses on the possibility that some well-known voting procedures lead to specific types of monotonicity paradoxes in preference profiles that are characterized by the presence and election of a Condorcet winner. Moulin’s theorem establishes the incompatibility of Condorcet-consistency ... see more
20 Voting Procedures Designed to Elect a Single Candidate
20 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 Co... see more
Introduction
Voting paradoxes occur in particular profile domains. For the avoidance of the paradoxes it is therefore important to know if the profiles typically encountered in practice are of such nature that the paradoxes are very unlikely or downright impossible. Ever since the publication of Arrow’s theorem,... see more
The (In)Vulnerability of 20 Voting Procedures to the Preference Inversion Paradox in a Restricted Domain
Responsiveness to electoral opinions is one of the hallmarks of democratic governance. We focus on a particularly strong type of unresponsiveness, viz., one where the complete inversion of all preferences in the electorate is accompanied with no change in the electoral outcome. It is known that the ... see more
The (In)Vulnerability of 20 Voting Procedures to Lack of Monotonicity in a Restricted Domain
This chapter focuses on the possibility that some well-known voting procedures lead to specific types of monotonicity paradoxes in preference profiles that are characterized by the presence and election of a Condorcet winner. Moulin’s (Journal of Economic Theory 45:53–64, 1988) theorem establishes t... see more
The (In)Vulnerability of 20 Voting Procedures to the Inconsistency Paradox (aka Reinforcement Paradox) in a Restricted Domain
This chapter focuses on the possibility that some well-known voting procedures are vulnerable to the Inconsistency paradox even in preference profiles that are characterized by a restricted domain where a Condorcet winner exists and is elected in each disjoint subset of voters but not in their union... see more
Which of 20 Voting Procedures Satisfy or Violate the Subset Choice Condition (SCC) in a Restricted Domain?
The relative desirability of a voting procedure is assessed, inter alia, by verifying which axioms, or postulates, it satisfies or violates. One of these axioms is the subset choice condition (SCC). This axiom requires that if a candidate, x, is elected under a given voting procedure, f, in a profil... see more
The (In)Vulnerability of 20 Voting Procedures to the No-Show Paradox in a Restricted Domain
The No-Show paradox occurs whenever a group of identically-minded voters is better off abstaining than by voting according to its preferences. Moulin’s (Journal of Economic Theory 45:53–64, 1988) result states that if one wants to exclude the possibility of the No-Show paradox, one has to resort to ... see more
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