Pareto efficiency: Difference between revisions
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{{wikipedia|Pareto efficiency}} |
{{wikipedia|Pareto efficiency}} |
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'''Pareto efficiency''' (frequently referred to as the "'''Pareto criterion'''" or "'''Unanimity criterion'''" in the [[election method]] context) is a basic criterion for evaluating [[voting system|voting systems]]. It can be defined in this way: |
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{{definition|If every voter prefers alternative X over alternative Y, then the |
{{definition|If every voter prefers alternative X over alternative Y, then the election method prefers X over Y}} |
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This criterion is important in the context of [[Arrow's impossibility theorem]]. |
This criterion is important in the context of [[Arrow's impossibility theorem]], since it was one of Arrow's criteria in the theorem. |
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Virtually every devised election method satisfies this criterion. An example of a method which would fail it would be ''Random Candidate'', where some candidate is elected at random, regardless of the submitted votes. |
Virtually every devised election method satisfies this criterion. An example of a method which would fail it would be ''Random Candidate'', where some candidate is elected at random, regardless of the submitted votes. |
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Revision as of 04:27, 10 September 2022
Pareto efficiency (frequently referred to as the "Pareto criterion" or "Unanimity criterion" in the election method context) is a basic criterion for evaluating voting systems. It can be defined in this way:
If every voter prefers alternative X over alternative Y, then the election method prefers X over Y
This criterion is important in the context of Arrow's impossibility theorem, since it was one of Arrow's criteria in the theorem.
Virtually every devised election method satisfies this criterion. An example of a method which would fail it would be Random Candidate, where some candidate is elected at random, regardless of the submitted votes.
A second, stronger variation of the criterion (meaning it implies the first variation of the criterion as well) is "if at least one voter prefers X over Y, and no voters prefer Y over X, then the system prefers X over Y."
Independence of Pareto-dominated alternatives (IPDA) says that if one option (X) wins an election, and a new alternative (Y) is added, X will win the election if Y is Pareto-dominated (using the second version of the criterion).
The Pareto criterion is Hare-PSC in the single-winner case.