Proportional representation: Difference between revisions
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==Non-Partisan Definitions==
* Under the
* Under the [[Monroe's method | Monroe interpretation]], voting is an attribution problem where every candidate has a [[Quota | quota
* Under the Thiele interpretation, every voter has an honest utility of each candidate, and even if you completely resent a candidate, it is statistically impossible for your honest utility of any individual candidate to equal 0 exactly. Under this interpretation, the more an outcome maximizes the sum among all voters: ln( the sum of utilities that voter gave to each winner), the more proportional it is. Since candidates can’t choose their honest utilities, they can choose the scores they give to candidates which means that it is much more likely that a candidate will give a set of candidates all zero scores which will blow up the natural log function (see footnote), so to counter-act this, the most Thiele voting methods instead use the partial sums of the harmonic function, which are closely related to the natural log (The natural log is the integral of 1/t from t=1 to t=x and the partial sums of the harmonic series are the summation of 1/n from n=1 to n=x).
* 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 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.
The Monroe interpretation named after the first first person to formalize the concept, Burt Monroe.<ref name="Monroe 1995 pp. 925–940">{{cite journal | last=Monroe | first=Burt L. | title=Fully Proportional Representation | journal=American Political Science Review | publisher=Cambridge University Press (CUP) | volume=89 | issue=4 | year=1995 | issn=0003-0554 | doi=10.2307/2082518 | pages=925–940|url=https://www.cambridge.org/core/journals/american-political-science-review/article/fully-proportional-representation/ACD79636D5CF12D1E56D43EF7AB7AFE2 | access-date=2020-02-09}}</ref> [[Single transferable vote]] is a Monroe type system which predates this formalization so it is clear that the core idea had existed for some time.
[[Keith Edmonds]] saw a unification of [[Proportional representation|Proportional Representation]] and the concept of one person one vote which was maintained throughout winner the winner selection method. He coined the term "vote unitarity" for the second concept<ref>https://groups.google.com/forum/#!topic/electionscience/Tzt_z6pBt8A</ref> and designed a score reweighting system which satisfied both Hare Quota Criterion and Vote Unitarity. As such it would preserve the amount of score used through sequential rounds while attributing representation in a partitioned way similar to Monroe. It would assign Hare Quotas of score to winners which allowed for a voters influence to be spread over multiple winners as opposed to Monroe which assigns a whole ballot with no spreading. Since score is a conserved quantity which is spent like money there is a natural analogy to [https://rangevoting.org/MarketBasedVoting.html Market based voting]. This concept was heavily influence by economic theory not the Monroe interpretation even though the resultant mathematical formulation is quite similar.
===Comparison===
Many of the properties of these systems can be derived from their party list simplifications. The [[Balinski–Young theorem]] implies that not all desirable properties are possible in the same system. Theile type systems reduce to [[Highest averages method|divisor methods]] which means that adding voters or winners will not change results in undesirable ways. The other three reduce to [[Largest remainder methods]] which obey Quota Rules but adding voters or winners may change outcomes in undesirable ways. One such way is failure of [[Participation criterion]]. It is not clear which is a fundamentally better choice since Quota Rules are inanimately tied with some definitions of proportionality.
Phragmen and Monroe share many desirable and undesirable properties. Most importantly a lack of convexity, the ability for votes that give every candidate the same score to affect the outcome. There are also election scenarios where both philosophies pick what is clearly the wrong winner. Further details can be found in the “Pereira’s Complaints about Monroe” section of [https://rangevoting.org/MonroeMW.html Monroe’s method] or the “Major defect pointed out by Toby Pereira” section of this [http://scorevoting.net/PRintLinprog.html Phragmen-Type method])
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However neither not{{clarify}} fail the [http://scorevoting.net/QualityMulti.html#faildesid universally liked candidate criterion] which is a criterion that Thiele type methods fail.
'''Benefits of the Phragmen/Monroe/Unitary measure of proportionality:'''
Passes the ULC criteria. For Thiele-type methods, because they fail ULC, every time a candidate that every voter gave a max rating to wins, the distribution of the remaining winners becomes more majoritarian/utilitarian.
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