Difference between revisions of "Proportionality for Solid Coalitions"

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Looking at the top 5 lines, 50 voters, a Hare quota, mutually most prefer the set of candidates (A1-5) over all other candidates, so Hare-PSC requires at least one of (A1-5) must win. (Note that Sequential Monroe voting fails Hare-PSC in this example. However, one could forcibly make SMV do so by declaring that the candidate with the highest Monroe score within the set (A1-5) must win the first seat, for example.) <ref>https://forum.electionscience.org/t/an-example-of-maximal-divergence-between-smv-and-hare-psc/586</ref>
Generally, Droop-PSC makes it more likely that a majority will win at least half the seats than only Hare-PSC. The reason for this is that majority solid coalitions always constitute enough DroolDroop quotas to always win at least half the seats, while with Hare quotas they can only guarantee they will win just under half the seats and have over half a Hare quota to win the additional seat required to get at least half the seats. 5-winner example using STV with Hare quotas:
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<blockquote>So, the Hare quota here is 20. A1 and A2 are immediately elected, but post-transfer A3 only has 11 votes, and is thus eliminated first. B1, B2, B3 take the remaining 3 seats.<ref>https://www.reddit.com/r/EndFPTP/comments/ermb1s/comment/ff7a7f8</ref></blockquote>
There can be quota overlaps when assigning PSC claims; suppose a group constituting 80% of a quota of voters vote A>B>C>=D, another group of 80% of a quota vote B>A>C>=D, and another group of 50% of a quota vote C>A=B=D. Then, 2 candidates must be elected from the set (A, B, C, D), since in total 2.1 quotas mutually most prefer that set, but a further constraint is that 1 candidate must win from within (A, B), since 1.6 quotas mutually most prefer them. It would not satisfy PSC if the final winner set had neither A or B in it in other words, even if it had C and D.
== Generalised solid coalitions ==
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