Approval voting: Difference between revisions
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Fully strategic Approval voting with perfectly informed voters generally elects the [[Condorcet winner]], and more generally, someone from the Smith set; this is because a plurality of voters have an incentive to set their [[Approval threshold|approval thresholds]] between the Smith candidate and the most-viable non-Smith candidate, resulting in at least the same approval-based margin as the Smith candidate has in their [[head-to-head matchup]] against the non-Smith candidate. A common argument for Approval>[[Condorcet methods]] is that when voters are honest, they get a utilitarian outcome, while if they are strategic, they at least get the CW. This not being as much the case with [[Score voting]] or [[STAR voting]], it is not possible to figure out who the CW is from Approval ballots, since only limited [[pairwise counting]] information can be inferred. |
Fully strategic Approval voting with perfectly informed voters generally elects the [[Condorcet winner]], and more generally, someone from the Smith set; this is because a plurality of voters have an incentive to set their [[Approval threshold|approval thresholds]] between the Smith candidate and the most-viable non-Smith candidate, resulting in at least the same approval-based margin as the Smith candidate has in their [[head-to-head matchup]] against the non-Smith candidate. A common argument for Approval>[[Condorcet methods]] is that when voters are honest, they get a utilitarian outcome, while if they are strategic, they at least get the CW. This not being as much the case with [[Score voting]] or [[STAR voting]], it is not possible to figure out who the CW is from Approval ballots, since only limited [[pairwise counting]] information can be inferred. |
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Here is an example of finding the Approval voting result, and its ranking of all candidates, using [[pairwise counting]] and the [[Smith set ranking]]: <blockquote>30 AB |
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20 BC |
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10 ADE |
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20 BCE </blockquote>If the pairwise counting is done by looking at the margins on each voter's ballot, rather than the winning votes/approvals directly (i.e. in the A vs B matchup, the AB voters are recorded as having no preference, since they approve both candidates, but do have a preference for A>C in the A vs C matchup because they approve one candidate and not the other), then the table is: |
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{| class="wikitable" |
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|+ |
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!Ranking of candidates |
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! |
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!B |
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!A |
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!C |
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!E |
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!D |
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|- |
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|1st |
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|B |
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| --- |
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|'''20 (+10 Win)''' |
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|'''30 (+30 Win)''' |
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|'''50 (+40 Win)''' |
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|'''50 (+40 Win)''' |
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|- |
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|2nd |
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|A |
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|10 (-10 Loss) |
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| --- |
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|40 (Tie) |
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|'''30 (+10 Win)''' |
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|'''30 (+30 Win)''' |
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|- |
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|2nd |
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|C |
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|0 (-30 Loss) |
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|40 (Tie) |
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| --- |
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|'''20 (+10 Win)''' |
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|'''40 (+30 Win)''' |
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|- |
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|3rd |
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|E |
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|10 (-40 Loss) |
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|20 (-10 Loss) |
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|10 (-10 Loss) |
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| --- |
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|'''20 (+20 Win)''' |
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|- |
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|4th |
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|D |
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|10 (-40 Loss) |
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|0 (-30 Loss) |
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|10 (-30 Loss) |
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|0 (-10 Loss) |
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| --- |
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|} |
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This could also be done by treating each voter's Approval ballot as a ranked ballot where all approved candidates are equally ranked 1st and all other candidates are ranked last. This shows how Approval can be thought of as a Condorcet method where every candidate must be ranked either 1st or last. |
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==See also== |
==See also== |