Majority: Difference between revisions
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''Derived from an e-mail by James Green-Armytage'' |
''Derived from an e-mail by James Green-Armytage'' |
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== Criticism |
== Criticism of this scheme == |
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While criteria 2-4 above are popular, only criterion 2 (the [[Majority criterion for solid coalitions]] a.k.a. the [[Mutual majority criterion]]) deals with "majority" in the sense of "more than half of the voters," and even this criterion applies only in the peculiar special case that more than half of the voters rank the same set of candidates uninterrupted, in some order, in the top positions of the ballot. |
While criteria 2-4 above are popular, only criterion 2 (the [[Majority criterion for solid coalitions]] a.k.a. the [[Mutual majority criterion]]) deals with "majority" in the sense of "more than half of the voters," and even this criterion applies only in the peculiar special case that more than half of the voters rank the same set of candidates uninterrupted, in some order, in the top positions of the ballot. |
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Criteria 3 and 4 (the [[Condorcet criterion]] and [[Smith set|Smith criterion]]) only deal with a "majority" in the sense of "more than half of the voters expressing an opinion between two given candidates." They don't make any assurance that a "majority" in the stronger sense will take precedence over a "majority" in this weaker sense. |
Criteria 3 and 4 (the [[Condorcet criterion]] and [[Smith set|Smith criterion]]) only deal with a "majority" in the sense of "more than half of the voters expressing an opinion between two given candidates." They don't make any assurance that a "majority" in the stronger sense will take precedence over a "majority" in this weaker sense. |
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== An alternative majority rule criterion == |
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An alternative criterion to these four might guarantee that a majority of the voters (in the sense of "more than half of the voters") with a given preference (such as, "candidate A is preferable to candidate B") can always prevail over the other voters, simply by voting sincerely, without having to use a strategic vote. |
An alternative criterion to these four might guarantee that a majority of the voters (in the sense of "more than half of the voters") with a given preference (such as, "candidate A is preferable to candidate B") can always prevail over the other voters, simply by voting sincerely, without having to use a strategic vote. |
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This property doesn't imply satisfaction of any of the above criteria except for criterion 1, and none of the above criteria implies this property. |
This property doesn't imply satisfaction of any of the above criteria except for criterion 1, and none of the above criteria implies this property. |
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In the following methods, a majority sincerely preferring A to B can ensure that B loses merely by voting for A and not voting for B: [[Approval voting]], [[Bucklin voting]], the [[River]] method, the [[Schulze method]] and [[Ranked Pairs]] (assuming with these that defeat strength is measured as the number of voters favoring the winning side). Most methods with an [[Approval voting|approval]] base also |
In the following methods, a majority sincerely preferring A to B can ensure that B loses merely by voting for A and not voting for B: [[Approval voting]], [[Bucklin voting]], the [[River]] method, the [[Schulze method]] and [[Ranked Pairs]] (assuming with these that defeat strength is measured as the number of voters favoring the winning side). Most methods with an [[Approval voting|approval]] base also possess it. |
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The following methods lack this property: [[Plurality voting|Plurality]], [[Borda count]], [[IRV|instant runoff voting]], and [[Minimax|Minmax]]. Also, methods which don't allow voters to "not vote for" some candidates would lack this property. |
The following methods lack this property: [[Plurality voting|Plurality]], [[Borda count]], [[IRV|instant runoff voting]], and [[Minimax|Minmax]]. Also, methods which don't allow voters to "not vote for" some candidates would lack this property. |
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== Majority rule |
== Majority rule criteria based on beatpaths == |
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If more voters prefer candidate A to candidate B, then A ''pairwise beats'' B, and the ''strength'' of this pairwise win is equal to the literal number of voters who rank A above B. (It is possible to define ''strength'' in other ways, but not for this purpose.) |
If more voters prefer candidate A to candidate B, then A ''pairwise beats'' B, and the ''strength'' of this pairwise win is equal to the literal number of voters who rank A above B. (It is possible to define ''strength'' in other ways, but not for this purpose.) |
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