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#REDIRECT [[Approval cutoff#Preference-approval]]<br /> |
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A [[preference-approval]] is a [[preference order]] that combines preference with approval. It can contain either weak or strong preferences. A complete preference-approval is a [[total preference order]]. |
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==Rationality Restrictions== |
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Here are some rationality restrictions on preference-approvals. Suppose there exists two alternatives, x and y: |
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1) If a given voter prefers x over y, and approves y, then she must approve x. |
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2) If a given voter prefers x over y, and does not approve x, then she must not approve y. |
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3) If a given voter is indifferent between x and y, and approves x, then she must approve y. |
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4) If a given voter is indifferent between x and y, and does not approve x, then she must approve y. |
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He are some expressions of preference-approvals and translations into natural language: |
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|x>y: "The voter prefers x over y, but approves neither." |
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|x=y: "The voter is indifferent between x and y, but approves neither." |
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x|y: "The voter prefers x over y, but only approves x." |
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x>y|: "The voter prefers x over y, but approves both." |
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[[Steven Brams]] and [[Peter Fishburn]] used preference-approvals in their book "Approval Voting" in 1983, though it probably was used before then. |
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There are 2, 8, 44, 308, ... different preference-approvals for 1, 2, 3, 4, ... candidates (Sloan's [http://www.research.att.com/~njas/sequences/A005649 A005649]). |
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==Sources== |
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Brams, Steven J. & Fishburn, Peter C. ''Approval Voting''. Cambridge, MA: Birkhäuser, Boston, 1983. |
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[[Category:Voting theory]] |
[[Category:Voting theory]] |
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Latest revision as of 00:49, 22 April 2020
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