Proportional STAR voting

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There are various ways to turn the single-winner voting method STAR voting into a proportional representation method. Here is one:

Repeat the following steps until all seats are filled:

  • Find the STAR winner using the current ballots.
  • Sort the ballots: first, from highest to lowest rating for the winner; then, within each of those groups, from lowest to highest by the runner-up; then, within groups that are identical on both of those, from lowest to highest by the second runner-up (the third highest score); etc.
  • Remove the first Hare quota of ballots (which are satisfied by the winner)

This is a monotonic, Droop-proportional method that reduces to STAR voting in the single-winner case.