# Difference between revisions of "Plurality criterion"

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<p><em>If the number of ballots ranking ''A'' as the first preference is greater than the number of ballots on which another candidate ''B'' is given any preference, then ''A''<nowiki>'</nowiki>s probability of election must be greater than ''B''<nowiki>'</nowiki>s.</em></p> | <p><em>If the number of ballots ranking ''A'' as the first preference is greater than the number of ballots on which another candidate ''B'' is given any preference, then ''A''<nowiki>'</nowiki>s probability of election must be greater than ''B''<nowiki>'</nowiki>s.</em></p> | ||

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+ | The reasoning behind this criterion is that, if A has more first preferences than B has any kind of preferences, it's intuitively implausible that there could be a good reason to elect B instead of A. | ||

<h4 class=left>Complying Methods</h4> | <h4 class=left>Complying Methods</h4> | ||

<p>[[Plurality voting|First-Preference Plurality]], [[Approval voting]], [[IRV]], and many [[Condorcet method|Condorcet methods]] (using winning votes as defeat strength) satisfy the Plurality criterion. [[Condorcet method|Condorcet methods]] using margins as the measure of defeat strength fail it, as do [[Raynaud]] regardless of the measure of defeat strength, and also [[Minmax|Minmax(pairwise opposition)]].</p> | <p>[[Plurality voting|First-Preference Plurality]], [[Approval voting]], [[IRV]], and many [[Condorcet method|Condorcet methods]] (using winning votes as defeat strength) satisfy the Plurality criterion. [[Condorcet method|Condorcet methods]] using margins as the measure of defeat strength fail it, as do [[Raynaud]] regardless of the measure of defeat strength, and also [[Minmax|Minmax(pairwise opposition)]].</p> |

## Revision as of 21:14, 22 March 2005

#### Statement of Criterion

*If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is given any preference, then A's probability of election must be greater than B's.*

The reasoning behind this criterion is that, if A has more first preferences than B has any kind of preferences, it's intuitively implausible that there could be a good reason to elect B instead of A.

#### Complying Methods

First-Preference Plurality, Approval voting, IRV, and many Condorcet methods (using winning votes as defeat strength) satisfy the Plurality criterion. Condorcet methods using margins as the measure of defeat strength fail it, as do Raynaud regardless of the measure of defeat strength, and also Minmax(pairwise opposition).