User:Jameson Quinn/SPARTA voting

"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. Until all seats are filled, repeat the following steps:
   1. Using the current ballots and their weights, find the two "frontrunners", the candidates with the highest total scores.
   2. For each of these two frontrunners, order the ballots from highest scoring to lowest scoring, and find the candidate's "constituent score": their score on the ballot one Droop quota in. Whichever frontrunner has the higher constituent score gets a seat.
      1. If there is a tie, break it using total 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 ballots.
      1. All ballots which score the winner higher than their constituent score are fully exhausted.
      2. All ballots which score the winner at exactly their constituent score are treated equally, partially exhausted.
         1. First, calculate the fraction F of each of these ballots that must be exhausted in order to exhaust one Droop quota overall.
         2. Any scores on these ballots which are higher than 5-5F are set to 5-5F.

Note that this reweighting does not require keeping "weights" separate from "scores". It simply uses up the ballot from the top down. Thus, for instance, a ballot which has exhausted 40% of its voting power (60% power remaining) cannot have any scores higher than 3, because 3 is 60% of 5.