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=October 2015
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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**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.
*Under the [[COWPEA]] interpretation, the weight received by a candidate approved on a particular ballot would not be equal to the other candidates also approved on that ballot, but in a proportional manner according to the rest of the electorate.
===Comparison===
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|[[Sequential Monroe voting]]||[[Monroe's method | Monroe interpretation]]||-
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|[[Method of Equal Shares]]||[[Monroe's method | Monroe interpretation]]||-
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|[[Sequentially Spent Score]]||[[Vote unitarity | Unitary interpretation]]||-
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|[[Sequentially Shrinking Quota]]||[[Vote unitarity | Unitary interpretation]]||May not be strictly Unitary but follows from the theory
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|[[Sequential proportional approval voting]]||[[Proportional approval voting | Thiele Interpretation]]||Approval ballots only
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|[[Reweighted Range Voting]]||[[Proportional approval voting | Thiele Interpretation]]||May not be strictly Thiele but follows from the theory
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|[[Single distributed vote]]||[[Proportional approval voting | Thiele Interpretation]]||A more Thiele implementation of [[Reweighted Range Voting]]
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|[[Sequential proportional score voting]]||[[Proportional approval voting | Thiele Interpretation]]||
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|[[Harmonic Voting]]||[[Proportional approval voting | Thiele Interpretation]]||
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|[[Sequential Phragmen]]||[[Phragmén's Method| Phragmén interpretation]]||
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|[[Sequential Ebert]]||[[Phragmén's Method| Phragmén interpretation]]||
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|[[PAMSAC]]||[[Phragmén's Method | Phragmén interpretation]]||
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|[[COWPEA Lottery]]||[[COWPEA| COWPEA interpretation]]||
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The trouble with this is, politicians are not like tap water and oranges. That reasoning would make sense if politicians were “wholly owned” by the Blues, just as Peter wholly-eats an apple. But even the most partisan politicians in Canada do a lot of work to help Joe Average constituent whose political leanings they do not even know. At least, so I am told.
===Incompatibility of the philosophies===
Pick your poison: it seems that all proportional voting methods must fail one of two closely related properties:
# If a group of voters gives all the candidates the same score, that cannot affect the election results (ex: if you gave every candidate a max score, your vote shouldn’t change who is and isn’t a winner any more so than you would change the results by just not voting).
# If some of the winners are given the same score by all voters, that cannot affect the proportionality of the election results among the remaining winners (ex: if you removed a candidate that is given a max score by all voters, and ran the election again such that you were electing 1 less winner, the only difference between that election result and the original election result should be that it does not contain the universally liked candidate).▼
▲If some of the winners are given the same score by all voters, that cannot affect the proportionality of the election results among the remaining winners (ex: if you removed a candidate that is given a max score by all voters, and ran the election again such that you were electing 1 less winner, the only difference between that election result and the original election result should be that it does not contain the universally liked candidate).
Phragmen/Monroe-type methods fail 1. and Thiele-type methods fail 2. and as of this point, it doesn’t seem possible to have them both without giving up PR.
Peters and [[Piotr Skowron | Skowron]] determined other properties that Phragmén passes but no Thiele-type method can pass, further indicating an incompatibility between the Phragmén and Theile philosophies.<ref name="Peters Skowron 2019">{{cite arXiv | last=Peters | first=Dominik | last2=Skowron | first2=Piotr | title=Proportionality and the Limits of Welfarism | date=2019-11-26 | eprint=1911.11747 | class=cs.GT}}</ref>
== Notes ==
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