Condorcet's paradox and anonymous preference profiles

  title={Condorcet's paradox and anonymous preference profiles},
  author={William V. Gehrlein and Peter C. Fishburn},
  journal={Public Choice},
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… 

Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences*

Many studies have considered the probability that a pairwise majority rule (PMR) winner exists for three candidate elections. The absence of a PMR winner indicates an occurrence of Condorcet's

Uniform generation of anonymous and neutral preference profiles for social choice rules

An exact formula for the number of equivalence classes of preference profiles (called roots) in the Impartial Anonymous and Neutral Culture model of social choice is derived, and a symbolic algebra routine that can be used for Monte-Carlo algorithms for the study of various structural properties of SCRs is described.

The Chairman’s Paradox Revisited

This paper re-examines the so-called ‘chairman’s paradox’ and replaces the standard assumption of linear preference orders with weak preference orders, which allow for indifference, and points to a new paradox of sophisticated voting.

A Note on the Likelihood of the Absolute Majority Paradoxes

For three-candidate elections, we compute under the Impartial Anonymous Culture assumption, the conditional probabilities of the Absolute Majority Winner Paradox (AMWP) and the Absolute Majority

On the (Sample) Condorcet Efficiency of Majority Rule: An alternative view of majority cycles and social homogeneity

The Condorcet efficiency of a social choice procedure is usually defined as the probability that this procedure coincides with the majority winner (or majority ordering) in random samples, given a

Multi-winner scoring election methods: Condorcet consistency and paradoxes

The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality, k-Negative Plurality, k-Borda, and Bloc. These four election methods are extensions of usual scoring

The impact of dependence among voters’ preferences with partial indifference

Standard weighted scoring rules do not directly accommodate the possibility that some voters might have dichotomous preferences in three-candidate elections. The direct solution to this issue would

On the Condorcet efficiency of approval voting and extended scoring rules for three alternatives

The results presented in this chapter belong to the long tradition of evaluating the voting rules on their propensity to select the Condorcet winner. This tradition dates back to de Borda (1781), who

The Impartial, Anonymous, and Neutral Culture Model: A Probability Model for Sampling Public Preference Structures

The Impartial, Anonymous, and Neutral Culture Model allows for a testbed that can be used to answer various questions about the properties and behaviors of anonymous and neutral social choice rules for large parameters and the results of two Monte Carlo experiments are presented.



Majority Decision-Making with Partial Unidimensionality

  • R. Niemi
  • Economics
    American Political Science Review
  • 1969
A major dilemma for majority decision-making occurs when the summation of transitive individual preference orderings results in an intransitive social ordering. The problems posed by this phenomenon,

Some mathematical remarks on the paradox of voting

When a group of m individuals endeavours to choose a winner from a set of n alternatives by making all possible pairwise comparisons among the alternatives (using simple majority rule), there exists


IN THIS PAPER we consider procedures for going from several individual preferences among several alternatives, called candidates, to something which may be called a collective preference. The

A mathematical solution for the probability of the paradox of voting.

Through the use of this model, a general solution for the probability of the paradox is derived, together with an approximation for computational convenience, and some numerical results are given.

The Probability of a Cyclical Majority

Consider a committee or society attempting to order the alternatives (X_1, X_2, X_3) by use of majority rule. Each individual is assumed to have a strong ordering (called a profile) on the

Voter concordance, simple majorities, and group decision methods

This paper examines the effect of the degree of agreement among voters' preferences, as measured by the Kendall-Smith coefficient of concordance, on (1) the likelihood that one decision alternative

An analysis of simple two‐stage voting systems

The propensities of alternative two-stage systems to elect the candidate which would be elected by a theoretically more sophisticated but less practical norm procedure such as simple majority of the Borda sum-of-ranks method are assessed.

The Theory of Committees and Elections.

I The Theory of Committees and Elections.- I. A Committee and Motions.- II. Independent Valuation.- III. Can a Motion be Represented by the same Symbol on Different Schedules?.- IV. A Committee using

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

Social Choice and Individual Values

Originally published in 1951, Social Choice and Individual Values introduced "Arrow's Impossibility Theorem" and founded the field of social choice theory in economics and political science. This new