Proportionality for Solid Coalitions: Difference between revisions

Content added Content deleted
VisualWikitext
No edit summary
No edit summary
Line 1: Line 1:
'''Proportionality for Solid Coalitions''' ('''PSC''') is a criterion for proportional methods requiring that sufficiently-sized groups of voters (solid coalitions) always elect a proportional number of candidates from their set of mutually most-preferred candidates. In general, any time any group of voters prefers any set of candidates over all others, a certain minimum number of candidates from that set must win to pass the criterion, and the same must hold if the preferred set of candidates for a group can be shrunk or enlargened. It is the main conceptualization of Proportional Representation generally used throughout the world ([[Party List]] and [[STV]] pass versions of it.)
'''Proportionality for Solid Coalitions''' ('''PSC''') is a criterion for proportional methods requiring that sufficiently-sized groups of voters (solid coalitions) always elect a proportional number of candidates from their set of mutually most-preferred candidates. In general, any time any group of voters prefers any set of candidates over all others, a certain minimum number of candidates from that set must win to pass the criterion, and the same must hold if the preferred set of candidates for a group can be shrunk or enlargened. It is the main conceptualization of Proportional Representation generally used throughout the world ([[Party List]] and [[STV]] pass versions of it.)


The main types of PSC are:
⚫
The two main types of PSC are k-PSC (aka. Hare-PSC, 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) and k+1-PSC (aka. Droop-PSC, which is the same as Hare-PSC but holding for Droop quotas instead). The Droop-PSC criterion is also called the '''Droop proportionality criterion'''. Note that Droop proportionality implies the [[Mutual majority criterion|mutual majority criterion]].

=== Hare-PSC ===
k-PSC (aka. Hare-PSC, 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) and

=== Droop-PSC ===
⚫
k+1-PSC (aka. Droop-PSC, which is the same as Hare-PSC but holding for Droop quotas instead). 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.


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.
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.
Retrieved from "https://electowiki.org/wiki/Proportionality_for_Solid_Coalitions"