﻿

The voting paradox (also known as Condorcet's paradox or the paradox of voting) is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic (i.e. not transitive), even if the preferences of individual voters are not. This is paradoxical, because it means that majority wishes can be in conflict with each other. When this occurs, it is because the conflicting majorities are each made up of different groups of individuals.

For example, suppose we have three candidates, A, B, and C, and that there are three voters with preferences as follows (candidates being listed in decreasing order of preference):

Voter First preference Second preference Third preference
Voter 1 A B C
Voter 2 B C A
Voter 3 C A B

If C is chosen as the winner, it can be argued that B should win instead, since two voters (1 and 2) prefer B to C and only one voter (3) prefers C to B. However, by the same argument A is preferred to B, and C is preferred to A, by a margin of two to one on each occasion. The requirement of majority rule then provides no clear winner.

Also, if an election were held with the above three voters as the only participants, nobody would win under majority rule, as it would result in a three way tie with each candidate getting one vote. However, Condorcet's paradox illustrates that the person who can reduce alternatives can essentially guide the election. For example, if Voter 1 and Voter 2 choose their preferred candidates (A and B respectively), and if Voter 3 was willing to drop his vote for C, then Voter 3 can choose between either A or B - and become the agenda-setter.

When a Condorcet method is used to determine an election, a voting paradox among the ballots can mean that the election has no Condorcet winner. The several variants of the Condorcet method differ on how they resolve such ambiguities when they arise to determine a winner. Note that there is no fair and deterministic resolution to this trivial example because each candidate is in an exactly symmetrical situation.

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Paradox of voting — This article is about the contention that an individual s vote will probably not affect the outcome. For the arguably irrational results that can arise in a collective choice among three or more alternatives, see Voting paradox. Part of the… …   Wikipedia

• Voting system — For other uses, see Voting system (disambiguation). Part of the Politics series Electoral methods …   Wikipedia

• Paradox — For other uses, see Paradox (disambiguation). Further information: List of paradoxes A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition. Typically,… …   Wikipedia

• Voting — Vote redirects here. For the Finno Ugric people, see Votes …   Wikipedia

• Comparison of instant runoff voting to other voting systems — This article is a comparison of various voting systems with Instant runoff voting (IRV), also called the Alternative Vote , preferential voting and ranked choice voting. Contents 1 Categories 2 Voting system criteria 3 Voting system results …   Wikipedia

• Apportionment paradox — An apportionment paradox exists when the rules for apportionment in a political system produce results which are unexpected or seem to violate common sense. To apportion is to divide into parts according to some rule, the rule typically being one …   Wikipedia

• Instant-runoff voting — Example instant runoff voting ballot …   Wikipedia

• Proxy voting — Part of the Politics series Electoral methods Single winner …   Wikipedia

• Condorcet-Paradox — Das Condorcet Paradoxon (auch „Problem der zyklischen Mehrheiten“, „Arrow s Paradox“ oder „paradox of voting“ genannt) ist ein nach Marie Jean Antoine Nicolas Caritat, Marquis de Condorcet benanntes Paradoxon bei Wahlverfahren, das sich vor allem …   Deutsch Wikipedia

• Arrow paradox (disambiguation) — Arrow paradox may mean: *Zeno s paradox about infinity and the movement of an arrow *Kenneth Arrow s impossibility theorem about social choice and voting *Kenneth Arrow s fundamental paradox of information: its value for the purchaser is not… …   Wikipedia