Proportionality for Solid Coalitions: Difference between revisions
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'''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.) |
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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'''. |
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]]. |
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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. |
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Any voting method that collects enough information to distinguish solid coalitions (generally scored or ranked methods, since preferences can be inferred from their ballots) can be forced to be PSC-compliant by first electing the proportionally correct number of candidates from each solid coalition before doing anything else. |
Any voting method that collects enough information to distinguish solid coalitions (generally scored or ranked methods, since preferences can be inferred from their ballots) can be forced to be PSC-compliant by first electing the proportionally correct number of candidates from each solid coalition before doing anything else. |