Proportionality for Solid Coalitions: Difference between revisions

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=== Hare-PSC ===
k-PSC or Hare-PSC is a condition requiring a solid coalition of c candidates supported by k Hare quotas to be always elect at least <math>\min(c, k)</math> most-preferred candidates I(i.e. k candidates whenever c is not less than k.)
 
=== Droop-PSC ===
k+1-PSC or Droop-PSC (since many authors call the [[Hagenbach-Bischoff quota]] a Droop quota) is the same as Hare-PSC but holds for Droop[[Hagenbach-Bischoff quota|Hagenbach-Bischoff quotas]] instead, and requires the solid coalition to be supported by ''more'' than k HB quotas, rather than at least that amount. The Droop-PSC criterion is also called the '''Droop proportionality criterion'''. Note that Droop proportionality implies the [[mutual majority criterion]].
 
=== Hagenbach-Bischoff-PSC ===
[[Hagenbach-Bischoff quota|Hagenbach-Bischoff]]-PSC is the same as Droop-PSC but holds for HB quotas instead, and only requires that the candidates supported by the solid coalition either tie or win when they are each preferred by exactly one HB quota.
 
The main difference between Hare-PSC and Droop-PSC can be seen with an example: Suppose you can buy two boxes of pizza, with over 2/3rds of voters wanting Cheese pizza, and under 1/3rds of the voters wanting Pepperoni pizza. Hare-PSC would say that you should buy at least one box of Cheese pizza, but has no opinion on what you should buy for the second box, whereas Droop-PSC would say that you should buy two boxes of Cheese pizza. This can be explained as happening partially because if the 2/3rds group of cheese-preferring voters split themselves into two equally sized groups of over 1/3rd of voters each, then these "two" groups that want Cheese would each outnumber the group of under 1/3rds of voters that want Pepperoni.