Proportional approval voting: Difference between revisions
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{{Wikipedia}}
'''Proportional approval voting''' (PAV) is a
PAV works by looking at how "satisfied" each voter is with each potential result or outcome of the of the election.
The satisfaction for individual voters of a potential result is calculated based on how many of the successful candidates they voted for. In this particular system, if an individual voted for ''n'' successful candidates (and an irrelevant number of unsuccessful ones) then their satisfaction is taken to be
: <math>1
Adding up the satisfaction of all the voters with the potential result gives the total satisfaction with that result. The potential result with the highest total satisfaction is chosen as the actual result.
If there was only one winner then ''proportional approval voting'' would become simple ''[[approval voting]]''. Alternatively, if each voter only voted for all the candidates of a single party then the results would essentially be the same as the [[D'Hondt method]] of ''[[party-list proportional representation]]''. The method can also be used with [[Sainte-Laguë method|Sainte-Laguë]] divisors.
Without the weighting of satisfaction, i.e. if the numbers of votes for each candidate are simply added up and those with the highest numbers elected, equivalent to satisfaction being ''n'', then this would amount to ''[[block approval voting]]'' which could have a similar chance of landslide results as ''[[block voting]]''.
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A somewhat simpler counting method is '''sequential proportional approval voting''' where candidates are elected one-by-one to the winners' circle by approval voting, but in each round the value of the votes of each voter who already has ''m'' candidates in the winners' circle is reduced to
: <math>\frac{1}{m
This was developed by the Danish polymath Thorvald N. Thiele, and used (with adaptations) in [[Sweden]] for a short period after [[1909]].
The system disadvantages minority groups who share some preferences with the majority. In terms of [[tactical voting]], it is therefore highly desirable to withhold approval from candidates who are likely to be elected in any case, as with [[cumulative voting]] and the [[single non-transferable vote]].
PAV is strongly [[Monotonicity|monotonic]] and passes [[Independence of Irrelevant Ballots]] (IIB). However, it fails the [[Universally liked candidate criterion]] (ULC) and also [[Perfect representation|Perfect Representation In the Limit]] (PRIL), which is arguably a prerequisite for an approval method to be considered properly proportional.
== Example ==
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! !! AB !! AC !! AD !! BC !! BD !! CD
|-
| voters approving 2 successful candidates (satisfaction of 1
|-
| voters approving 1 successful candidate (satisfaction of 1) || 17 || 5 || 30 || 22 || 13 || 25
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== Similar Systems ==
Both the [[Phragmén's Method]] and [[w:Sequential_proportional_approval_voting|Sequential Proportional Approval Voting]] are very similar systems invented in the early 1900s. [[Reweighted Range Voting]] is
Optimised PAV is the version of the method that allows any number of candidates to be elected according to the optimal candidate weights, rather than a fixed number with equal weight. It is not known if this method passes PRIL, but on the assumption that is does, it has been considered, along with [[COWPEA]], as a candidate method for the most accurately proportional approval method.<ref>{{Cite journal|last=Pereira|first=Toby|date=2023-05-17|title=COWPEA (Candidates Optimally Weighted in Proportional Election using Approval voting)|url=https://arxiv.org/abs/2305.08857|journal=arXiv}}</ref> Optimised PAV Lottery elects a fixed number of candidates with equal weight, using the candidate weights as probabilities, and it has parallels with COWPEA Lottery. If it does pass PRIL, then it would pass the four main Holy Grail criteria of PRIL, strong monotonicity, IIB and ULC, along with COWPEA Lottery.
== References ==
<references />
{{fromwikipedia}}
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[[Category:Proportional voting methods]]
[[Category:Multi-winner voting methods]]
[[Category:Approval
[[Category:Approval PR methods]]
[[Category:Highest averages-reducing voting methods]]
[[Category:Adjustable-proportionality voting methods]]
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