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User:Jameson Quinn/SPARTA voting: Difference between revisions

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User:Jameson Quinn/SPARTA voting (view source)

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# Voters score each candidate in the district from 0-5.
# 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.
##On each ballot, initialize the "remaining score" for each candidate to equal the original score for that candidate. Later, if the ballot is partially exhausted, that remaining score may change, but the original score will not.
# Until all seats are filled, repeat the following steps:▼
##To begin with, the "max remaining score" for each ballot is 5.
## Using the current ballots and their weights, findFind the two "frontrunners", the candidates with the highest total "remaining scores".▼
▲# Until all seats are filled, repeat the following steps:
###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.
▲## Using the current ballots and their weights, find the two "frontrunners", the candidates with the highest total remaining scores.
####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).
## For each of these two frontrunners, order the ballots from highest to lowest original score, and find the candidate's "constituent score": their original score on the ballot one Droop quota (of max remaining score) from the top. Whichever frontrunner has the higher constituent score gets a seat.
###For Ifeach thereof isthese atwo tiefrontrunners, breakfind ittheir using"threshold totalscore": remainingthe highest score. (Possiblesuch alternativethat tiebreakers:there totalare scoreone overquota theof topremaining Droopvoter quotapower of ballots; or,which totalgive overthem topthat twoscore Droopor quotas of ballots)higher.
###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.
## Exhaust one Droop quota of max remaining score.▼
### 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)
### All ballots which score the winner higher than their constituent score are fully exhausted.▼
▲## Exhaust one Droop quota of max remaining score.
▲### All ballots which score(originally) scored the winner higher than their constituentthreshold score are fully exhausted (That is, remaining voting power becomes 0.)
### All ballots which score the winner at exactly their constituent score are treated equally, partially exhausted.
#### First, calculate the fraction E of each of these ballots that must be exhausted in order to exhaust one Droop quota overall. Use this to calculate the new maxof remaining score on the ballotoverall. If the previous max remaining score on the ballot was M, the new maximum will be M-ME
####Any remaining scores on these ballots which are higher thanMultiply the max remaining scorevoting arepower setof toeach theof maxthese remainingballots by score(1-E).
 
 
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) will have a max remaining score of 3 (60% of the original maximum 5).
 
[[Category:Multi-winner voting methods]]
[[Category:Proportional voting methods]]
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