Proportional representation: Difference between revisions

The backstory: Thiele, a danish statistician, and Phragmen, a mathematician (and yes, oddly enough Thiele was the statistician and Phragmen was the mathematician, not the other way around), 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 afterwards in order to make the number of seats parties won match their support even more closely. Phragmen believed there was 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 6]. Thiele also came up with the approval ballot version of harmonic voting, and it would take about a century for both his sequential proportional approval voting method, 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 were lost to history until about a century later when they were independently rediscovered.

I lumped Phragmen and Monroe together in the title, because these two philosophies share many desirable and undesirable properties: mainly a lack of convexity (i.e. the weak monotonicity described on the document), the ability for votes that give every candidate the same score to effect the outcome, this (Read 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 2]) haunting election scenario where both philosophies pick what is clearly the wrong winner, and not failing the [http://scorevoting.net/QualityMulti.html#faildesid universally liked candidate criterion 8] (which is a criterion that Thiele type methods fail).

Passes the ULC criteria 8. 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.

If a group of voters gives all the candidates the same score, that cannot effect 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 then you would change the results by just not voting)

If some of the winners are given the same score by all voters, that cannot effect 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).