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. In Mathematics, the word transitive admits at least three distinct meanings A group G acts transitively on a This is paradoxical, because it means that majority wishes can be in conflict with each other. A paradox is a true statement or group of statements that leads to a Contradiction or a situation which defies intuition; or inversely 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 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. A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is which always selects the Condorcet winner, the candidate The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters The several variants of the Condorcet method differ on how they resolve such ambiguities when they arise to determine a winner. A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is which always selects the Condorcet winner, the candidate Note that there is no fair and deterministic resolution to this trivial example because each candidate is in an exactly symmetrical situation.
The phrase "Voter's Paradox" is sometimes[1] used for the rational choice theory prediction that voter turnout should be 0. Rational choice theory, also known as rational action theory, is a framework for understanding and often formally modeling social and economic behavior Voter turnout is the percentage of eligible voters who cast a Ballot in an Election.
See also
- Kenneth Arrow, Section 1 with an example of a distributional difficulty of intransitivity + majority rule
- Arrow's impossibility theorem
- Gibbard-Satterthwaite theorem
- Independence of irrelevant alternatives
- Smith set
- Social Choice and Individual Values
- Voting system
References
- ^ Follow the Trend or Make a Difference: The Evolution of Stated Opinions, pages 3 and 7, Fang Wu and Bernardo A. Kenneth Joseph Arrow (born August 23, 1921) is an American Economist and joint winner of the Nobel Memorial Prize in Economics In Social choice theory, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system can convert the ranked preferences of individuals Independence of irrelevant alternatives (IIA is a term for an Axiom of Decision theory and various social sciences In Voting systems the Smith set is the smallest non-empty set of candidates in a particular election such that each member beats every other candidate outside the set in a pairwise Kenneth Arrow 's Monograph Social Choice and Individual Values (1951 2nd ed A voting system allows voters to choose between options often in an Election where candidates are selected for public office. Huberman, HP Laboratories, September 25, 2007.
External links
- Paradox of Majority Rule, a Madisonian rendering
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