Difference between revisions of "Proportionality for Solid Coalitions"

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=== Weak forms of PSC ===
Most methods that pass weak forms of PSC (i.e. any method that passes a weak form of Droop-PSC) allow a [[majority]] to strategically vote to get at least half of the seats. The more candidates there are that are preferred by a solid coalition, however, the less likely this may be; for example, [[Approval voting]] will likely pass the [[majority criterion]] in practice more often than the [[mutual majority criterion]], because things like the [[chicken dilemma]] may encourage voters to not approve all solidly supported candidates.
 
PSC is a requirement that holds for honest voters. Many voting methods pass weaker requirements that hold only for strategic voters, with the difficulty of the strategy depending on the method. In general, any method that passes such weaker versions of PSC is considered to be at least semi-proportional. Note that PSC implies all of these weaker forms of PSC. Here are some of these weaker requirements (note that the requirements vary slightly depending on whether you're using the Hare quota, HB quota, or other quota):
* with rated, approval, and choose-one ballots, all of the candidates in the set are given the maximum score or are marked.)
<blockquote>If a solid coalition of k quotas evenly distributes its support among k of their preferred candidates such that each of the k candidates receives maximal support from a quota of voters, with each quota of voters giving no support to any other candidates, and the solid coalition as a whole giving no support to any candidates other one of the k candidates, then at least k of their preferred candidates must win.</blockquote>[[SNTV]] and [[Cumulative voting|cumulative voting]] pass this with Droop quotas.<blockquote>If a solid coalition of k quotas gives maximal support to k of their preferred candidates, and no support to all other candidates, then at least k of their preferred candidates must win.</blockquote>Most cardinal PR methods pass this for Hare quotas.<blockquote>If a solid coalition of k quotas gives maximal support to at least k of their preferred candidates, and less-than-maximal support to all other candidates, at least k of those preferred candidates must win.</blockquote>[[Sequential Monroe voting]] passes this, making it the best cardinal PR method from the perspective of PSC. This is probably the strongest PSC-like requirement that a natural voting method can pass without actually passing PSC.
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== Examples ==
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