Proportionality for Solid Coalitions: Difference between revisions

<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 name="reddit 2011">{{cite web | title=Can Ranked-Choice Voting Save American Democracy? : EndFPTP | website=reddit | date=2011-01-26 | url=https://www.reddit.com/r/EndFPTP/comments/ermb1s/comment/ff7a7f8 | access-date=2020-02-19}}</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.

 

 

== Notes ==

With rated ballots, it is possible for a voter to express less-than-full support for any candidate. Because of this, one way to apply PSC to rated ballots and thus cardinal PR methods would be to require that every voter in each solid coalition give at least one candidate in their coalition the maximum score. An even stricter requirement could be to require them to give every candidate in the coalition a perfect score, though this could instead be thought of as a genuinely slightly weaker form of PSC; it is already satisfied by [[SMV]]. This is modeled off of the [[Majority criterion for rated ballots|majority criterion for rated ballots]].

 

Droop-PSC implies Hare-PSC, since a Hare quota is simply a large Droop quota, but the same doesn't hold the other way around. Hare-PSC is equivalent to the unanimity criterion and Droop-PSC to the mutual majority criterion in the single-winner case. Note that this means cardinal PR methods can only pass Hare-PSC and not Droop-PSC in order to reduce to cardinal methods that fail the mutual majority criterion in the single-winner case, which is most of them.

 

Though Droop-PSC guarantees a majority half of the seats, it doesn't guarantee a plurality group half the seats when it could take them using [[vote management]]. 5-winner example:

 

The HB quota is (110/(5)+1)=~18.333, so A is guaranteed only (51/18.333 rounded down) = 2 out of the 5 seats, less than half. With vote management, Party A could split into 3 groups of 17 votes each, and most PR methods would then give them 3 seats. So it may be worth considering a stronger type of Droop-PSC based on giving solid coalitions at least as many seats as they'd get in [[D'Hondt]]. [[Schulze STV]] is an example of a method that does so.

 

Note that PSC doesn't hold if some voters in a coalition back out-of-coalition candidates i.e. 1-winner example with Droop quota of 51:

 

Arguably there is some kind of coalition of 45 voters backing candidates A through J here, and since the largest opposing coalition is 8 voters, D'Hondt would say that the 45-voter coalition ought to win all 5 seats. At that point, one could eliminate all candidates outside the 45-voter coalition (K and L) at which point A through E all are a Hare quota's 1st choice and must all win. This sort of thinking is generally what Condorcet PR methods such as Schulze STV do.

 

Properties analagous to PSC can be considered for multi-winner voting methods that aren't proportional. For example, [[Bloc voting|Bloc Score voting]] guarantees that a majority solid coalition can elect all of its preferred candidates if they set their [[approval threshold]] between their preferred candidates and all other candidates.

 

== See Also ==