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{{rename|from=Cardinal PR|to=Cardinal proportional representation}}
 
'''Cardinal proportional representation''' (or "'''Cardinal PR'''") is a class containing [[cardinal voting systems]] used for [[proportional representation]] in multi-seat elections.
 
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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]].
 
===Example Systemssystems===
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[[Proportionality for Solid Coalitions]] is praised for ensuring that voters get what would intuitively be considered an at least somewhat proportional outcome, but is criticized for focusing too much on giving a voter one "best" rep
===The backstory===
Thiele, a Danish statistician, and Phragmen, a mathematician have been debating these two philosophies in Sweden. Thiele originally proposed [[Sequentialsequential Proportionalproportional Approvalapproval Votingvoting]] 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.
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