Minimax Condorcet

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In voting systems, the Minimax method is one of several Condorcet methods used for tabulating votes and determining a winner when using preferential voting in a single-winner election. It is also known as the Simpson-Kramer method, and the successive reversal method.

Minimax selects the candidate for whom the greatest pairwise score for another candidate against him is the least such score among all candidates.

Formally, let score(X,Y) denote the pairwise score for X against Y. Then the candidate, W selected by minimax (aka the winner) is given by:

W = arg min _X(max _Yscore(Y,X))

When it is permitted to rank candidates equally, or to not rank all the candidates, three interpretations of the rule are possible. When voters must rank all the candidates, all three rules are equivalent.

The score for candidate x against y can be defined as:

1. The number of voters ranking x above y, but only when this score exceeds the number of voters ranking y above x. If not, then the score for x against y is zero. This is sometimes called winning votes.
2. The number of voters ranking x above y minus the number of voters ranking y above x. This is called using margins.
3. The number of voters ranking x above y, regardless of whether more voters rank x above y or vice versa. This interpretation is sometimes called pairwise opposition.

When one of the first two interpretations is used, the method can be restated as: "Disregard the weakest pairwise defeat until one candidate is unbeaten." An "unbeaten" candidate possesses a maximum score against him which is zero or negative.

Minimax using winning votes or margins satisfies Condorcet and the majority criterion, but not the Smith criterion, mutual majority criterion, independence of clones criterion, or Condorcet loser criterion. When winning votes is used, Minimax also satisfies the Plurality criterion.

When the pairwise opposition interpretation is used, minimax also does not satisfy the Condorcet criterion. However, when equal-ranking is permitted, there is never an incentive to put one's first-choice candidate below another one on one's ranking. It also satisfies the Later-no-harm criterion, which means that by listing additional, lower preferences in one's ranking, one cannot cause a preferred candidate to lose.

See also

• Minimax - main minimax article
• Wald's maximin model - Wald's maximin model

External resources

• Description of ranked ballot voting methods: Simpson by Rob LeGrand
• Electowiki: minmax

This election-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Condorcet methods Election stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем решить контрольную работу MV John Hamilton Gray Misery Signals Look at other dictionaries: Minimax — This article is about the decision theory concept. For other uses, see Minimax (disambiguation). Minimax (sometimes minmax) is a decision rule used in decision theory, game theory, statistics and philosophy for minimizing the possible loss for a… …   Wikipedia Condorcet loser criterion — In single winner voting system theory, the Condorcet loser criterion is a measure for differentiating voting systems. It implies the majority loser criterion. A voting system complying with the Condorcet loser criterion will never allow a… …   Wikipedia Condorcet method — Part of the Politics series Electoral methods Single winner …   Wikipedia Condorcet criterion — Part of the Politics series Electoral methods Single winner …   Wikipedia Método de Condorcet — Un Método de Condorcet es un sistema de votación para elegir a una persona entre un grupo de candidatos. Los votantes ordenan de mayor a menor preferencia a los candidatos. Hay muchos métodos diferentes que cumplen la condición para ser… …   Wikipedia Español 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 Instant-runoff voting — Example instant runoff voting ballot …   Wikipedia Independence of irrelevant alternatives — Cette page est la traduction de la page Wikipedia anglaise Independence of Irrelevant Alternatives (IIA) (Independance des Alternatives Irrelevantes) est un axiome des théories décisionelles utilisé en science sociale. Quoique les formulations de …   Wikipédia en Français Indépendance des alternatives non-pertinentes — L indépendance des alternatives non pertinentes (en anglais Independence of Irrelevant Alternatives ou IIA) est un axiome des théories décisionnelles utilisé en science sociale. Quoique les formulations de l IIA varient, elles ont comme point… …   Wikipédia en Français Later-no-harm criterion — The later no harm criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less preferred candidate cannot cause a more… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”