Difference between revisions of "Proportionality for Solid Coalitions"

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:
Methods that reduce to [[D'Hondt]] in the [[Party list case|party list case]]<nowiki/>tend to pass at least a weak form of Droop-PSC; this is because D'Hondt guarantees every party will get at least the number of HB quotas it has rounded down.
51 A>C
49 B
10 C
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. With vote management, Party A could split into 3 groups of 18 or 19 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 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: