Plurality distortion and majority rule

A desirable property of a collective choice procedure in human groups is that its outcome should be clear‐cut. The plurality and Condorcet procedures are investigated under a variety of conditions to determine their susceptibility to indecisiveness. Both plurality indecision and Condorcet indecision can attain a large likelihood of occurrence when group size is small. However, both likelihoods, but especially the latter's, prove highly volatile in the presence of minor variations in group size when group size is small. In general, the relative decisiveness of the two procedures fluctuates as a function of the pattern of the group's preference probabilities. An exception is groups of four and six members where plurality indecision is always less likely than Condorcet indecision. When it is required that the plurality winner receive more than 50 percent of the votes, the probability of Condorcet indecision is always less than or equal to the probability of plurality indecision, irrespective of the pattern of the group's preference probabilities.

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confidence: 99%

Collective Indecision

Gillett

1977

“…Paris (1975) offers the "tentative" hypothesis that "the probability of plurality distortion is inversely related to the probability of the paradox." Since the paradox of voting does not occur in single-peaked cultures (Black, 1958;Sen, 19701, the probability of plurality distortion in such cultures should always be fairly high if Paris's hypothesis holds.…”

Section: Culture Most Likely To Produce Plurality/condorcet Disagreementmentioning

confidence: 98%

“…However, they confined their attention to the equiprobable culture and to certain nonspecific cultures. Paris (1975) points to the importance for democratic theory of several, as yet unexplored, avenues for research in this area:…”

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confidence: 98%

“…Such an event, in which the plurality winner does not correspond with the Condorcet winner, was termed "plurality distortion" by Paris (1975). Paris obtained the probability of plurality distortion, in the case of three alternatives, for small groups of about 20 members and for a variety of cultures (probability distributions on the preference orderings, representing the inclinations of the individual voter).…”

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confidence: 99%

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The asymptotic likelihood of agreement between plurality and condorcet outcomes

Gillett

1980

This article deals 4 t h collective decision making by voting procedures in living systems at the levels of groups, organizations, societies, or supranational systems. General principles are outlined which permit the determination of the likelihood of agreement, and disagreement, between plurality and Condorcet outcomes when system size is large, for any number of alternatives in virtually any culture. A method is developed which ascertains, for any number of alternatives, the system in which the likelihood of plurality/Condorcet disagreement reaches a maximum. The hypothesis that an inverse relation exists between the probability of plurality distortion and the probability of the paradox of voting is disproved. Methodological issues arising from previous work are considered. In pairwise simple majority contests, A1 defeats Az by 13 votes to 7, Az defeats A3 by 12 votes to 8, and A3 defeats A1 by 11 votes to 9. Thus, there is intransitivity in the social ordering, in the form of a cyclical majority, and no Condorcet winner emerges. Consequently, no alternative can be said to represent the will of the majority. The cyclical majority problem, known also as the paradox of voting, has generated a substantial body of research concerning both the conditions for its occurrence (e.g., Black, 1958;Sen, 1970) and the likelihood of its occurrence (e.g., Gehrlein & Fishburn, 1976; Gillett, 1977Gillett, , 1978May, 1971).A method of collective choice which does not give rise to the paradox of voting is the plurality procedure. The winner under this scheme is the alternative which receives the largest number of fist preference votes.Thus, in the previous example, application of the plurality procedure results in the emergence of a clear-cut winner, A1, with 8 first preference votes. However, by concentrating on first preferences, the plurality system fails to take into account all the information contained in the voters' preference orderings. Consequently, it suffers from the disadvantage that it sometimes selects an alternative over which at least one other alternative is preferred by a simple majority of voters. That is, collective 23

“…The most common concern in these studies is whether the winner of the election under a given procedure (plurality, plurality with runoff, Borda point count, and so forth) is the candidate who would defeat every other candidate on the basis of pairwise majority comparisons, given that such a "majority candidate" exists. Examples include Fishburn (1971Fishburn ( , 1974, Fishburn & Gehrlein (1976, 1982, Gehrlein & Fishburn (1978a, 1978b, Paris (1975), Gillett (1980aGillett ( , 1980b, and Chamberlin & Cohen (1978). The last of these uses one of the more sophisticated generating models, which is based on a four-dimensional spatial model of voter preferences and allows varying degrees of similarity among candidates.…”

Section: Introductionmentioning

confidence: 97%

Empirical comparisons of voting procedures

Fishburn

1986

This article considers decision making in living systems at the levels of the organization, society, or supranational system. It examines voting data from 48 elections over a four-year period that are used to compare different social choice and ranking procedures. Each election had four to six nominees and approximately 1,000 voters. The data indicate that most elections had a majority candidate and that this candidate did not have the most first-place votes about 10 to 20% of the time. Rankings of nominees were compared for the plurality, Hare, and Australian preference procedures. With five nominees, the plurality and Hare rankings differed about 28% of the time, the plurality and Australian preference rankings differed about 55% of the time, and the Hare and Australian preference rankings differed about 62% of the time.Although the data came from a very different source than data previously analyzed by Coombs, Cohen, and Chamberlin (1984). the present conclusions agree closely with theirs in areas where comparisons can be made.