Difference between revisions of "Approval voting"

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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.
 
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
 
20 BC
 
10 ADE
 
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:
{| class="wikitable"
|+
!Ranking of candidates
!
!B
!A
!C
!E
!D
|-
|1st
|B
| ---
|'''20 (+10 Win)'''
|'''30 (+30 Win)'''
|'''50 (+40 Win)'''
|'''50 (+40 Win)'''
|-
|2nd
|A
|10 (-10 Loss)
| ---
|40 (Tie)
|'''30 (+10 Win)'''
|'''30 (+30 Win)'''
|-
|2nd
|C
|0 (-30 Loss)
|40 (Tie)
| ---
|'''20 (+10 Win)'''
|'''40 (+30 Win)'''
|-
|3rd
|E
|10 (-40 Loss)
|20 (-10 Loss)
|10 (-10 Loss)
| ---
|'''20 (+20 Win)'''
|-
|4th
|D
|10 (-40 Loss)
|0 (-30 Loss)
|10 (-30 Loss)
|0 (-10 Loss)
| ---
|}
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.
 
==See also==
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