Paradox Of Voting Research Articles

The Selfish Voter Paradox and the Thrown-Away Vote Argument

The probability that an individual's voting in a presidential election will determine the outcome being negligible, it is argued that participation is irrational if predicated on principles that are either egocentric or act-prospective. Voter participation, if rational, must rely on some over-arching principle that is (a) Sociotropic, (b) Axionomic, (c) Collective-distributive, and (d) Neutrofactual. A distinctively ethical component must be involved, such that all purely “economic,” “cost-benefit” models postulating selfish voter rationality are incoherent. The notion of “helping” to elect one's candidate is criticized and rejected unless formulated in a special way. An important pragmatic consequence of the analysis is that the idea (relied on by the two major parties) of “wasting one's vote” on a third party candidate is shown to be invalid or of more limited application than generally assumed. If a sizeable minority (e.g., college students) were educated to reject that argument, politics might be profoundly affected.

The Selfish Voter Paradox and the Thrown-Away Vote Argument

The probability that an individual's voting in a presidential election will determine the outcome being negligible, it is argued that participation is irrational if predicated on principles that are either egocentric or act-prospective. Voter participation, if rational, must rely on some over-arching principle that is (a) Sociotropic, (b) Axionomic, (c) Collective-distributive, and (d) Neutrofactual. A distinctively ethical component must be involved, such that all purely “economic,” “cost-benefit” models postulating selfish voter rationality are incoherent. The notion of “helping” to elect one's candidate is criticized and rejected unless formulated in a special way. An important pragmatic consequence of the analysis is that the idea (relied on by the two major parties) of “wasting one's vote” on a third party candidate is shown to be invalid or of more limited application than generally assumed. If a sizeable minority (e.g., college students) were educated to reject that argument, politics might be profoundly affected.

Computational Criteria for Voting Systems

Condorcet's paradox of voting and Arrow's impossibility theorem are by now well known. Inspired by Arrow's treatment of social choice, others have presented alternative proofs of his theorem and different impossibility results. Professor Fishburn has recently treated us to some interesting new voting paradoxes. It is important to have the area of inconsistency among the various treatments explored and clearly mapped out. It is equally important to come to terms with the known inconsistencies in order to construct a solid social choice edifice on safe ground. Coming to terms with the inconsistencies must surely mean deciding between alternative normative conditions when all of them cannot be satisfied simultaneously. This paper attempts to do just that by adding some computational criteria to the standard list of normative criteria and then singling out a subset as being more important (to the author at least) than the rest. Since the ‘important’ criteria are mutually consistent they can be used to derive some properties of democratic decision processes. Simple majority rule, applied in sequential elimination, is distinguished as the best collective decision method. It fails to satisfy the Pareto, or unanimity, criterion – one often regarded as a sine qua non of social choice – but when this condition is added to the author's list an impossibility result obtains. An argument is proposed to counter the suggestion that Pareto optimality be added to the list and some other condition removed.

THE OSTROGORSKI PARADOX: A PECULIARITY OF COMPOUND MAJORITY DECISION *

ABSTRACTIn the article it is shown that if during an election each voter picks the party with which he agrees on a majority of issues, it is nevertheless possible that a majority of voters disagrees with the winning majority party on every issue. This ‘inverted majority decision’, here called the Ostrogorski‐paradox, resembles the structure underlying the Condorcet paradox and Simpson's paradox. Each concerns a relation of pairwise decision or observation functioning in an n‐wise world.Our object here is to point out a possible paradox of parliamentary democracy, and to sketch some of its relationships to other paradoxes.

Remarks on the Theory of Collective Choice

Ever since the so-called paradox of voting was generalized by Arrow (1963) to every democratic method of collective decision-making, a vast literature has appeared (a) trying to circumvent Arrow's difficulty by weakening some of his conditions (Bordes, 1976; Hansson, 1973; Plott, 1973; Sen, 1969); (b) proposing some other paradoxes in the theory of collective choice (Batra and Pattanaik, 1972; Hansson, 1969; Schwartz, 1970; Sen, 1970a) and (c) casting doubts about the relevance of Arrow's theorem to the theory of Paretian welfare economics (Bergson, 1966; Little, 1952; Samuelson, 1967, 1977). The purpose of this paper is to make some remarks on these recent developments in the theory of collective choice. The first part of the paper deals with the question of how much one needs to weaken Arrow's collective rationality condition in order to avoid his impossibility result. As is well known, Arrow (1963) imposed the collective rationality condition that the society can arrange all conceivable alternatives in order of preference and that, if some available set of alternatives is specified, the society must choose therefrom the best alternative with respect to that preference ordering. We will consider two conditions of consistent choice which are weaker than that of Arrow. The first condition requires that, if an alternative x is chosen over another alternative y in binary choice, y should never be chosen from any set of alternatives that contain x; while the second condition requires that, if x is chosen over y in binary choice, there exists no choice situation in which y is chosen and x is available but rejected. (In the second case y can be chosen if x is also chosen, while in the first case y cannot be chosen anyway.) There seems to be a gulf that separates possibility from impossibility in between these two seemingly similar consistency conditions. It will be shown that the first consistency requirement is incomnpatible with essentially Arrovian conditions on the collective choice rule, while the second consistency condition is compatible with the same conditions. Although the difference between these consistency requirements is very subtle, the implication thereof in the context of impossibility result is therefore dramatically different. Lest we should be too satisfied, we must hasten to add that no collective choice rule satisfying our second consistency requirement can be free from the paradox of Paretian liberal (Sen, 1970a; Batra and Pattanaik, 1972). The Arrow-Sen theory is then contrasted with the Bergson-Samuelson one. In view of doing this, it is convenient to remember that Arrow's incompatible conditions on collective choice rule can be classified into two categories. The first category consists of statements that apply to any fixed profile of individual preference relations, while the second category refers to the responsiveness of the collective choice to the variations in profiles. (The first category embraces the condition of collective rationality and the Pareto rule, while the second category consists of the independence of irrelevant alternatives

The voter's paradox and the homegeneity of individual preference orders

The voter's paradox and the homegeneity of individual preference orders

The probability of the paradox of voting: A computable solution

The probability of the paradox of voting: A computable solution

MANAGERIAL DECISION MAKING UNDER INTRANSITIVE CONDITIONS: AN INTERNATIONAL STUDY OF THE VOTER'S PARADOX

ABSTRACTResearchers and scholars have been concerned for many years with the normative aspects of amalgamating individual preferences to form a group decision. The present paper studies how managers actually make decisions involving intransitive preference functions by examining how the Voter's Paradox Conflict (VPC) is actually resolved by homogeneous groups of subjects from five different populations (Denmark, England, Switzerland, U.S. Private, and U.S. Military). The results showed that level of cooperation, the reward structure (real versus imaginary money), and experience with the VPC are the major factors relating to the solution obtained. Nationality differences explained little of the variance in decision outcomes. Intrasitivity in preferences seems to be handled similarly by executives in the countries studied. Interpretations are drawn in the context of cooperative and competitive decision theory and for cross‐cultural decision research.

Condorcet's paradox and anonymous preference profiles

Condorcet's paradox [6] of simple majority voting occurs in a voting situation with n voters and m candidates or alternatives if for every alternative there is a second alternative which more voters prefer to the first alternative than conversely. The paradox can arise only if the strict simple majority relation on the alternatives is cyclic, provided that m is finite. Studies of the paradox are usually based either on profiles or A-profiles (anonymous preference profiles). A profile is a function that assigns a preference order on the alternatives to each voter. An A-profile, which has also been called a return [28], profile [31] and pattern [20], is a function that assigns a nonnegative number of voters to each potential preference order on the alternatives such that the sum of the assigned integers equals n. In general, many different profiles which retain voter identities map into the same A-profile, and any two profiles that map into the same A-profile bear the same simple majority relation on the alternatives. Hence, it may appear that it is purely a matter of personal taste or analytical convenience whether one works with profiles or with A-profiles in studying Condorcet's paradox. Although this is true in one sense, there are important differences between the two bases that will be explored in the present paper. Of special concern will be the fact that some A-profiles correspond to very few profiles (consider an A-profile that assigns all n voters to the same preference

The voter's paradox and the homogeneity of individual preference orders

The voter's paradox and the homogeneity of individual preference orders

Campaign Expenditures and Political Competition

THE theory of public choice emphasizes the role of economic assumptions in the mechanisms which generate political choices.1 In a recent contribution to this literature, Stigler has suggested that the "all-or-nothing" characterization of political competition is both unappealing and unrealistic. He is sympathetic to a basic similarity between political and economic competition, where, like the latter, the products of a political process (public policy) can be construed as ranging continuously from failure to success.2 Stigler notes that there has been a tendency to label (incorrectly) the winning of 51 per cent of legislative seats a victory and 49 per cent a defeat and argues that the success of a political party is "more or less," not all-or-none. Thus, the importance of a continuous characterization of political outcomes is that it reduces the apparent fundamental differences which have exacerbated the extent of the analogy between economic and political competition.3

Voter's paradox and logrolling

Voter's paradox and logrolling

A note on unconditional probabilities and the voter's paradox

A note on unconditional probabilities and the voter's paradox

Avoiding the voter's paradox democratically: Comment

Avoiding the voter's paradox democratically: Comment

Logrolling and the Paradox of Voting: Are They Really Logically Equivalent? A Comment

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VOTING PARADOXES:

The Political QuarterlyVolume 46, Issue 3 p. 304-309 VOTING PARADOXES: A Socratic Dialogue ANDREW M. COLMAN, ANDREW M. COLMAN * The first part of this dialogue appeared in the April-June issue this year. The authors are at the University of LeicesterSearch for more papers by this authorIAN POUNTNEY, IAN POUNTNEY * The first part of this dialogue appeared in the April-June issue this year. The authors are at the University of LeicesterSearch for more papers by this author ANDREW M. COLMAN, ANDREW M. COLMAN * The first part of this dialogue appeared in the April-June issue this year. The authors are at the University of LeicesterSearch for more papers by this authorIAN POUNTNEY, IAN POUNTNEY * The first part of this dialogue appeared in the April-June issue this year. The authors are at the University of LeicesterSearch for more papers by this author First published: July 1975 https://doi.org/10.1111/j.1467-923X.1975.tb02137.xCitations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume46, Issue3July 1975Pages 304-309 RelatedInformation

Plurality distortion and majority rule

Discussions of the implications of Arrow's theorem for majority rule have typically focused on calculating the probability of the paradox of voting. In doing so, these analyses have ignored another significant problem of preference aggregation in n-way (n > 2) elections, the existence of non-Condorcet winners, when a Condorcet alternative is available, under a simple plurality criterion. At the level of the democratic political system, e.g., a proposed national presidential primary or any electoral subsystem, e.g., state presidential primaries, gubernatorial, senatorial elections, the simple plurality criterion may distort electoral preferences by failing to select an available Condorcet candidate. An algorithm for calculating the probability of such plurality distortion is offered, and probability calculations for three-way elections for small electorates are presented. Most notable is the discovery that single-peaked preferences, while reducing or eliminating the probability of the paradox, lead to a concomitant increase in the probability of plurality distortion. In instances in which no candidate receives half the vote and preferences are single-peaked, the probability of plurality distortion is actually greater than the probability of plurality-Condorcet coincidence. These results cast some doubt on the validity of the plurality criterion as a voting procedure as well as indicating some of the difficulties inherent in the Condorcet criterion. Alternatives to the plurality criterion are discussed, and some preliminary tests of these alternatives are made.

Single-peakedness and guttman scales: Concept and measurement

Interest in dimensionality arises in both formal theory and empirical work. An important example of the theoretical results has to do with locating the optimal spatial strategy for a political candidate or party. As Anthony Downs and others have pointed out, the party seeking to win an election should move to the center of the voter distribution if, along with other conditions, the campaign is based on a single unidimensional issue continuum. Guttman scaling, factor analysis, and multidimensional scaling are among the many empirical techniques which have been devised to test unidimensionality. If these techniques indicate that attitudes on an issue are unidimensional, then the Downsian candidate should adopt the position of the median voter. Thus empirical data can be brought together with derivations from axiomatic theory to obtain optimal strategies for political parties. The empirical frequency of the paradox of voting provides another example of this combination of scaling techniques with formal theory. Duncan Black, for *University of Rochester and Ohio State University, respectively. We would like to thank Michael Coveyou for bringing to our attention one of the examples used in the paper.

Voter Antagonism and the Paradox of Voting

The purpose of this paper is to give a systematic account of the significance that antagonism among opinions of individuals has on the theory of social choice. We define an intensity of antagonism among individuals and an index of possibility of constructing social welfare functions, and show that when there is less antagonism in a society, then there is more possibility of constructing social welfare functions. Since antagonism is an opposite concept to similarity, this relation can be viewed as a formal realization of Arrow's assertion [1, Ch. 7] that sets preference similarity as the basis of social welfare judgement.

Avoiding the voter's paradox democratically

This paper is concerned with selecting an appropriate perspective from which to understand and evaluate social-decision procedures. Distinguishing between “agentrationality” and “option-rationality”, the author argues that a rational agent may choose a social-decision procedure that is not itself agent-rational (but merely option-rational). The argument puts the voter's paradox in a context allowing evaluation of (a) its general import and (b) practical proposals for avoiding it in particular cases. Arrow's four conditions for a social-decision procedure are shown to have little relevance to the understanding or evaluation of constitutions. The author concludes that the more fruitful perspective for discussing social-decision procedures is that of option-rationality rather than (as Arrow, Wolff, and others have supposed) that of agent-rationality.