# Condorcet's paradox and anonymous preference profiles

@article{Gehrlein1976CondorcetsPA, title={Condorcet's paradox and anonymous preference profiles}, author={William V. Gehrlein and Peter C. Fishburn}, journal={Public Choice}, year={1976}, volume={26}, pages={1-18} }

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…

## 156 Citations

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

- Economics
- 2002

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

- EconomicsMonte Carlo Methods Appl.
- 2009

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

- EconomicsSoc. Choice Welf.
- 2007

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

- Economics
- 2018

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

- Economics
- 2002

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

- Economics
- 2016

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

- Economics
- 2016

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

- Economics
- 2010

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

- Mathematics
- 2013

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.

## References

SHOWING 1-10 OF 26 REFERENCES

### Majority Decision-Making with Partial Unidimensionality

- EconomicsAmerican 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

- Mathematics
- 1971

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…

### AGGREGATION OF PREFERENCES WITH VARIABLE ELECTORATE

- Mathematics
- 1973

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.

- MathematicsBehavioral science
- 1968

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

- Mathematics
- 1970

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

- Economics
- 1973

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

- Economics
- 1976

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.

- Economics
- 1958

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

- Economics
- 1974

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

- Economics
- 1951

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…