<html><body><div style="color:#000; background-color:#fff; font-family:times new roman, new york, times, serif;font-size:12pt">Any single winner method that produces a societal ranking can be the basis for a proportional multi-winner method with a nice property. <br><br>For now, let's call the method the Societal Ranked Proportional method. (But maybe that is not a good name since the method does not produce a societal ranking it only uses it). The method is inspired by DMC.<br><br>Here is the nice property<br>For any n+1 candidate election for n seats that includes any or all of the n-seat SRP winners amongst the n+1 candidates, all SRP winners that are lower ranked than the lowest ranked SRP looser amongst the n+1 candidates, are guaranteed to win. <br>Corollary:<br>If all n SRP winners are
in any n+1 candidate election with one SRP loser, then each of the n SRP winners are either all
guaranteed to win or the one SRP winner that is displaced will be of higher societal ranking than the SRP looser that took its place.<br>Corollary:<br>If all n SRP winners are
in any n+1 candidate election with one SRP loser that is higher ranked than all of the SRP winners, then all of the SRP winners will win.<br><br>The n seat SRP method:<br>You need a societal ranking, such as from Schulze beat path, and
any proportional method, such as QPQ or STV, that can choose n winners from n+1 candidates
using the same ballots that produced the societal ranking. I recommend QPQ since you don't need to worry about adjusting
quotas.<br><br>Candidates are either hopeful, elected or excluded. All candidates are initially hopeful.<span style="mso-spacerun:yes"> </span>Do every possible n+1 candidate election for
n seats that includes all elected candidates (initially none), the lowest
ranked hopeful candidate, and any combination of other hopeful candidates.<span style="mso-spacerun:yes"> </span>If for any of these n+1 candidate elections the lowest ranked hopeful
candidate loses, set that candidate from hopeful to excluded.<span style="mso-spacerun:yes"> </span>Go on to the next lowest ranked hopeful
candidate.<span style="mso-spacerun:yes"> </span>If the lowest ranked hopeful
candidate is a winner of every n+1 candidate election that includes it and all
elected candidates, then set that candidate from hopeful to elected and go on
to the next hopeful candidate. Continue until n candidates are elected or the total
number of elected plus hopeful candidates equals n.<br><br>The method has the virtue of requiring fewer n+1 elections than other methods that are inspired by Condorcet single winner methods such as Schulze STV. It requires only one pass through the societal rankings. As soon as a candidate is declared excluded one does not need to calculate the results of any other n+1 elections in which it is a candidate. And as soon as one candidate is declared elected, no further n+1 candidate elections need be performed.<br><br><br> <br><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: times new roman,new york,times,serif; background-color: transparent; font-style: normal;" class="MsoNormal"><br></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: times new roman,new york,times,serif; background-color: transparent; font-style: normal;" class="MsoNormal"><br></div>
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