User:Jameson Quinn/SPARTA voting

From electowiki

"SPARTA voting" (a temporary working title that stands for "Scored Proportional Automatic Runoff with Top Allocation") is a proportional voting method based on score ballots. It works as follows, in multi-seat districts:

  1. Voters score each candidate in the district from 0-5.
  2. In step 3, we will be choosing winners and "using up" the voting power of the ballots which most helped them win. In order to do so, we begin by setting the "remaining voting power" (RVP) of each ballot to 1.
  3. Until all seats are filled, repeat the following steps:
    1. Find the two "frontrunners", the candidates with the highest total "remaining scores".
      1. To calculate a candidate's "remaining score" on each ballot: it is either their score on that ballot, or the maximum score times the remaining voting power on that ballot; whichever is less.
        1. Example: if a ballot with 0.7 remaining voting power scored 4 and 3 for candidates X and Y respectively, the remaining score for X would be 3.5 (0.7 * 5) and for Y would be 3 (the raw score, since it is less than 3.5).
    2. For each of these two frontrunners, find their "threshold score": the highest score such that there are one quota of remaining voter power of ballots which give them that score or higher.
      1. For example: let's say the quota was 10. If candidate X is rated 5 on 6 ballots with an RVP of 1.0, 6 ballots with an RVP of 0.5 (bringing total RVP so far to 9.0), and rated 4 on 6 ballots with an RVP of 1.0 (bringing total RVP to 12.0, and thus more than one quota), then their threshold score would be 4.
      2. If there is a tie (twe candidates with the same threshold score), break it using total remaining score. (Possible alternative tiebreakers: total score over the top Droop quota of ballots; or, total over top two Droop quotas of ballots)
    3. Exhaust one Droop quota of remaining score.
      1. All ballots which (originally) scored the winner higher than their threshold score are fully exhausted (That is, remaining voting power becomes 0.)
      2. All ballots which score the winner at exactly their constituent score are treated equally, partially exhausted.
        1. First, calculate the fraction E of each of these ballots that must be exhausted in order to exhaust one quota of remaining score overall.
        2. Multiply the remaining voting power of each of these ballots by (1-E).
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