Approval cutoff: Difference between revisions
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Another way to implement the approval threshold in practice would be to let voters mark approval of the candidates directly (similar to [[Approval voting]]) alongside their rankings, and then for whichever of the approved candidates the voter ranked lowest, all candidates ranked equal to or higher than that candidate are also considered approved. |
Another way to implement the approval threshold in practice would be to let voters mark approval of the candidates directly (similar to [[Approval voting]]) alongside their rankings, and then for whichever of the approved candidates the voter ranked lowest, all candidates ranked equal to or higher than that candidate are also considered approved. |
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== Preference-approval == |
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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. {{Clarify|reason=This seems like it should say "...then she must '''not''' approve y."?|date=April 2020}} |
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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." |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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==Total preference order== |
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A [[total preference order]] is a complete [[preference-approval]]. In other words, it is a preference-approval that contains all alternatives competing in a given election. |
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== Notes == |
== Notes == |
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The logic of the approval threshold is that if a voter approves a candidate, and they prefer some other candidate(s) over the candidate they approved, then it's very likely that voter would also approve of those more-preferred candidates if voting with an Approval ballot, since otherwise they'd be giving more support to a candidate they prefer less than the candidates they'd be disapproving. |
The logic of the approval threshold is that if a voter approves a candidate, and they prefer some other candidate(s) over the candidate they approved, then it's very likely that voter would also approve of those more-preferred candidates if voting with an Approval ballot, since otherwise they'd be giving more support to a candidate they prefer less than the candidates they'd be disapproving. |
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The [[preference-approval]] concept is highly related. |
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An approval threshold can be used in the context of rated methods as well. This can be useful for cardinal PR, since it could be possible to allow, for example, a Green Party voter to approve both Green Party candidates and Democratic candidates, using the approvals to ensure one of those preferred candidates wins, and then score the candidates in such a way as to maximize the odds that of the preferred candidates, one of the Green Party candidates wins. |
An approval threshold can be used in the context of rated methods as well. This can be useful for cardinal PR, since it could be possible to allow, for example, a Green Party voter to approve both Green Party candidates and Democratic candidates, using the approvals to ensure one of those preferred candidates wins, and then score the candidates in such a way as to maximize the odds that of the preferred candidates, one of the Green Party candidates wins. |
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See [[Smith//Approval]] for an example of the use of the approval threshold. |
See [[Smith//Approval]] for an example of the use of the approval threshold. |
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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:Ballot type]] |
[[Category:Ballot type]] |
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