Computer simulations of approval and plurality voting: The frequency of weak pareto violations and condorcet loser choices in impartial cultures

doi:10.1016/S0176-2680(86)80004-0

European Journal of Political Economy

Volume 2, Issue 1, 1986, Pages 47-59

https://doi.org/10.1016/S0176-2680(86)80004-0 Get rights and content

Summary

This article reports the results of computer simulations aiming at finding out the propensity of the approval and plurality voting to result in the choice of Condorcet losers under the impartial culture assumption. Moreover, simulations are conducted to find out the propensity of the approval voting to violate the weak Pareto criterion. In addition to the impartial culture assumption it is assumed that the voters vote sincerely and that in the approval voting the number of candidates the voter votes for, is randomly determined. Candidate and voter sets of various cardinality are investigated.

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Cited by (11)

A note on Approval Voting and electing the Condorcet loser
2016, Mathematical Social Sciences
Citation Excerpt :
Here, NPR is the voting rule that is also known as Anti-Plurality Rule, where each voter casts a vote against one candidate, and the candidate who receives the fewest negative votes is declared the winner. Notice that the IAC condition is to be contrasted with the Impartial Culture Condition (IC), on which most of the previous studies are based (Nurmi and Uusi-Heilkkilä, 1985; Gehrlein and Fishburn, 1978; Gehrlein and Lepelley, 1998).1 Under IC, the voters are assumed to vote in a completely independent way and the probability that any given voting situation will be observed is then given by a multinomial model.
Chapter 4 Voting procedures
2002, Handbook of Social Choice and Welfare
Voting procedures focus on the aggregation of individuals' preferences to produce collective decisions. In practice, a voting procedure is characterized by ballot responses and the way ballots are tallied to determine winners. Voters are assumed to have clear preferences over candidates and attempt to maximize satisfaction with the election outcome by their ballot responses. Such responses can include strategic misrepresentation of preferences.
Voting procedures are formalized by social choice functions, which map ballot response profiles into election outcomes. We discuss broad classes of social choice functions as well as special cases such as plurality rule, approval voting, and Borda's point-count method. The simplest class is voting procedures for two-candidate elections. Conditions for social choice functions are presented for simple majority rule, the class of weighted majority rules, and for what are referred to as hierarchical representative systems.
The second main class, which predominates in the literature, embraces all procedures for electing one candidate from three or more contenders. The multicandidate elect-one social choice functions in this broad class are divided into nonranked one-stage procedures, nonranked multistage procedures, ranked voting methods, and positional scoring rules. Nonranked methods include plurality check-one voting and approval voting, where each voter casts either no vote or a full vote for each candidate. On ballots for positional scoring methods, voters rank candidates from most preferred to least preferred. Topics for multicandidate methods include axiomatic characterizations, susceptibility to strategic manipulation, and voting paradoxes that expose questionable aspects of particular procedures.
Other social choice functions are designed to elect two or more candidates for committee memberships from a slate of contenders. Proportional representation methods, including systems that elect members sequentially from a single ranked ballot with vote transfers in successive counting stages, are primary examples of this class.
The Condorcet efficiency of approval voting and the probability of electing the Condorcet loser
1998, Journal of Mathematical Economics
The Condorcet winner in an election is an alternative that would defeat each of the other alternatives in a series of pairwise elections. The Condorcet efficiency of a voting rule is the conditional probability that the voting rule will elect the Condorcet winner, given that a Condorcet winner exists. The paper assumes the impartial culture condition for large electorates and shows that approval voting has greater Condorcet efficiency than plurality rule, and that it has smaller Condorcet efficiency than the voting rule in which voters must vote for half of the available alternatives. The likelihood that election rules select the Condorcet loser is also considered.
Chapter 30 Voting procedures
1994, Handbook of Game Theory with Economic Applications
The voting procedures used to elect candidates in large part determine whether elections are considered fair. The chapter focuses on the strategies that voters employ to try to effect better outcomes as long as they are allowed by the rules of a voting procedure. Voting procedures not only affect campaign strategies and electoral outcomes but also influence strategies and outcomes in legislatures, councils, and other voting bodies, wherein the alternatives that are voted on are not candidates but bills and resolutions. The chapter discusses how decision theory, and to a less extent game theory, can be used to illuminate the choice of better and worse strategies under different voting procedures. The strategic calculations that voters make result in outcomes that can be evaluated according to different normative criteria. The chapter describes some of the most important criteria that have been used to assess the quality of outcomes in voting bodies. Judgments about better and worse voting procedures can be made on the basis of these criteria. Preferential voting and proportional representation is described in the chapter that includes the Hare system of single transferable vote (STV), the Borda count, cumulative voting, and additional-member systems.
On the probability of electing the Condorcet
1993, Mathematical Social Sciences
We investigate the propensity of some simple voting systems to elect the Condorcet loser in three-alternative elections. Exact relations are obtained which give the probability of this paradox for plurality and negative voting as a function of the number of voters. Moreover, we show that, if preferences are single-peaked, then the Condorcet loser election is much less frequent with approval voting than with plurality voting.
Computer simulations of approval voting: Positional in one dimension candidates' characteristics
1988, European Journal of Political Economy

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^*: An earlier version of this paper was presented at the Nordic Political Science Association Workshop “Rationality, Legitimacy and Representation”, Marienhamn, Åland, May 13–15, 1985. The authors are grateful to Dr Gerald Doherty for checking the language of the present version and to the referees and editor of EJPE for comments. An enlarged version reporting the computation of some of the exact values of probabilities of criteria violations is available upon request.

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ArticleComputer simulations of approval and plurality voting: The frequency of weak pareto violations and condorcet loser choices in impartial cultures

Summary

European Journal of Political Economy

A note on the paradox of voting: anonymous preference profiles and May's formula

Public Choice

Strategic voting in Scandinavian parliaments

Scandinavian Political Studies

Comparison voting

Approval Voting

Social choice observed: five presidential elections of the American Psychological Association

The Journal of Politics

Borda's voting paradox: theoretical likelihood and electoral occurences

Behavioral Science

The paradox of voting: probability calculations

Behavioral Science

Mathematical derivation of an election system

Isis

Article
Computer simulations of approval and plurality voting: The frequency of weak pareto violations and condorcet loser choices in impartial cultures