# Difference between revisions of "Condorcet criterion"

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− | The '''Condorcet candidate''' or '''Condorcet winner''' of an [[election]] is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. Mainly because of Condorcet's [[voting paradox]], a Condorcet winner will not always exist in a given set of votes. | + | The '''Condorcet candidate''' or '''Condorcet winner''' of an [[election]] is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. On a one-dimensional [[political spectrum]], the Condorcet winner will be at the position of the median voter. Mainly because of Condorcet's [[voting paradox]], a Condorcet winner will not always exist in a given set of votes. |

The '''Condorcet criterion''' for a [[voting system]] is that it chooses the Condorcet winner when one exists. Any method conforming to the Condorcet criterion is known as a [[Condorcet method]]. | The '''Condorcet criterion''' for a [[voting system]] is that it chooses the Condorcet winner when one exists. Any method conforming to the Condorcet criterion is known as a [[Condorcet method]]. | ||

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<blockquote><table> | <blockquote><table> | ||

− | <tr><td align=right>499:</td><td align=left>A | + | <tr><td align=right>499:</td><td align=left>A>B>C</td></tr> |

− | <tr><td align=right>498:</td><td align=left>C | + | <tr><td align=right>498:</td><td align=left>C>B>A</td></tr> |

− | <tr><td align=right>3:</td><td align=left>B | + | <tr><td align=right>3:</td><td align=left>B>C>A</td></tr> |

</table></blockquote> | </table></blockquote> | ||

## Revision as of 21:58, 3 November 2006

The **Condorcet candidate** or **Condorcet winner** of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. On a one-dimensional political spectrum, the Condorcet winner will be at the position of the median voter. Mainly because of Condorcet's voting paradox, a Condorcet winner will not always exist in a given set of votes.

The **Condorcet criterion** for a voting system is that it chooses the Condorcet winner when one exists. Any method conforming to the Condorcet criterion is known as a Condorcet method.

## Complying methods

Black, Condorcet//Approval, Smith/IRV, Copeland, Llull-Approval Voting, Minmax, Smith/Minmax, ranked pairs and variations (maximize affirmed majorities, maximum majority voting), and Schulze comply with the Condorcet criterion.

Approval voting, Range voting, Borda count, plurality voting, and instant-runoff voting do not.

## Commentary

Non-ranking methods such as plurality and approval cannot comply with the Condorcet criterion because they do not allow each voter to fully specify their preferences. But instant-runoff voting allows each voter to rank the candidates, yet it still does not comply. A simple example will prove that IRV fails to comply with the Condorcet criterion.

Consider, for example, the following vote count of preferences with three candidates {A,B,C}:

499: A>B>C 498: C>B>A 3: B>C>A

In this case, B is preferred to A by 501 votes to 499, and B is preferred to C by 502 to 498, hence B is preferred to both A and C. So according to the Condorcet criteria, B should win. By contrast, according to the rules of IRV, B is ranked first by the fewest voters and is eliminated, and C wins with the transferred voted from B; in plurality voting A wins with the most first choices.

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