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. It is the main conceptualization of Proportional Representation generally used throughout the world ([[Party List]] and [[STV]] pass versions of it.) The two main types of PSC are k-PSC (aka. Hare-PSC, a condition requiring a solid coalition comprising k Hare quotas to be |
'''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. It is the main conceptualization of Proportional Representation generally used throughout the world ([[Party List]] and [[STV]] pass versions of it.) The two main types of PSC are k-PSC (aka. Hare-PSC, a condition requiring a solid coalition comprising k Hare quotas to be always elect at least k most-preferred candidates) and k+1-PSC (aka. Droop-PSC, which is the same as Hare-PSC but holding for Droop quotas instead). |
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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. |
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Looking at the top 5 lines, 50 voters, a Hare quota, mutually most prefer the set of candidates (A1-5) over all other candidates, so Hare-PSC requires at least one of (A1-5) must win. (Note that Sequential Monroe voting fails Hare-PSC in this example. However, one could forcibly make SMV do so by declaring that the candidate with the highest Monroe score within the set (A1-5) must win the first seat, for example.) <ref>https://forum.electionscience.org/t/an-example-of-maximal-divergence-between-smv-and-hare-psc/586</ref> |
Looking at the top 5 lines, 50 voters, a Hare quota, mutually most prefer the set of candidates (A1-5) over all other candidates, so Hare-PSC requires at least one of (A1-5) must win. (Note that Sequential Monroe voting fails Hare-PSC in this example. However, one could forcibly make SMV do so by declaring that the candidate with the highest Monroe score within the set (A1-5) must win the first seat, for example.) <ref>https://forum.electionscience.org/t/an-example-of-maximal-divergence-between-smv-and-hare-psc/586</ref> |
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== Generalised solid coalitions == |
== Generalised solid coalitions == |
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7 L</blockquote>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. |
7 L</blockquote>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. |
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