Cardinal proportional representation: Difference between revisions
Cardinal proportional representation (view source)
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Also see the following section for some categories.
When investigating cardinal PR, it is often categorized into optimal PR methods, which generally work by assigning every possible [[winner set]] a score based on how good it is, and picking the best winner set out of all possible winner sets, and sequential PR methods, which elect one candidate at a time. Optimal PR has the issue of being non-hand-countable and very computationally expensive and complex (in fact, with large committees, they may be both completely impossible to compute and very, very vulnerable to strategic voting<ref>{{Cite web|url=https://www.rangevoting.org/QualityMulti.html|title="Optimal proportional representation" multiwinner voting systems I: methods, algorithms, advantages, and inherent flaws|last=Smith|first=Warren D.|date=2015-10|website=rangevoting.org|url-status=live|archive-url=|archive-date=|access-date=}}</ref>), so in practice, many sequential cardinal PR methods are designed to approximate certain optimal PR methods. When simulating the quality of various cardinal PR methods, sometimes it's common to use optimal PR methods more as "benchmarks" of how good the winner set chosen by the sequential method is, rather than as an actual way of running an election.
The [[KP transform]] can be very useful in allowing '''Approval PR''' methods ([[Approval voting]]-based cardinal PR methods) to work with rated ballots with more than two allowed scores.
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*Under the [[Phragmén's Method| Phragmén interpretation]], voting is a distribution problem where the representation weight of candidates must be fairly spread across the different voters to produce the most equitable representation possible. The winner set composed of candidates which best distribute the candidates representation is the most proportional.
*Under the [[Monroe's method | Monroe
*Under the Thiele interpretation, voters have vote weight which should be distributed across candidates. The proportion of ballot weight assigned to each winner is the amount which that candidate supports their election. Under this interpretation, the more an outcome maximizes the sum of all score when reweighted by ballot weight, the more proportional it is.
**Thiele's [[party list case]] is the [[Highest averages method]]<nowiki/>s.
*Under the [[Vote unitarity | Unitary interpretation]] interpretation of each voter has an fixed amount of utility to be spent on candidates. When a candidate is elected their power to elect subsequent candidates is lower directly proportionally to the amount of utility previously spend on prior candidates. This interpretation can be thought of as an additional constraint on the [[Monroe's method | Monroe interpretation]] but since the philosophy is about voters spending points on candidates rather than voters themselves being assigned to candidates it is a distinct interpretation of proportional representation. The [[Vote unitarity | Unitary interpretation]] is in some way the inverse interpretation of the [[Phragmén's Method| Phragmén interpretation]]. In the former each '''voter''' has a conserved amount of vote weight to spend on candidates and in the latter the each '''candidate''' has a conserved amount of representation weight to distribute over the voters.
===Comparison===▼
To compare, [[PSC]] can be thought of to some extent as a separate philosophy to Monroe because rather than trying to look at utility, it requires coherent groups to have a certain number of seats. PSC and Monroe can be made to conflict with examples where a solid coalition has some differences within itself, while another, smaller group is more unified; see [[PSC#Examples]]. ▼
▲To compare, [[
[[Proportionality for Solid Coalitions]] is praised for ensuring that groups of voters get what would intuitively be considered an at least somewhat proportional outcome, even if they disagree about what candidate best represents their faction. Most methods passing this criterion behave like Monroe and don't use preferences outside the faction to decide who will be a faction's best representative, but exceptions like [[STV-CLE]] exist.
===Example systems===
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|[[Sequential Ebert]]||[[Phragmén's Method| Phragmén interpretation]]||
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▲===Comparison===
===The backstory===
Thiele, a Danish statistician, and Phragmen, a mathematician have been debating these two philosophies in Sweden. Thiele originally proposed [[sequential proportional approval voting]] in 1900 and it was adopted in Sweden in 1909 before Sweden switched to [[Party List]] voting afterward. Phragmen believed there were flaws in Thiele’s method, and came up with his own sequential method to correct these flaws, and that started [https://rangevoting.org/NonlinQuality.html#debate a debate about what was the ideal metric of proportionality]. Thiele also came up with the approval ballot version of [[harmonic voting]], however during that time the harmonic method was too computationally exhaustive to be used in a governmental election. Both his [[sequential proportional approval voting]] and his approval ballot version of the harmonic method was lost to history until about a century later when they were independently rediscovered.
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