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User:Jameson Quinn/SPARTA voting: Difference between revisions

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Easier-to-understand, but synonymous, explanation.
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m (RobLa moved page SPARTA voting to User:Jameson Quinn/SPARTA voting: Moving to user space for now; please feel free to move it back to the main namespace after it has some links to online discussions)
(Easier-to-understand, but synonymous, explanation.)
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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.
##To begin with, the "max remaining score" for each ballot is 5.
# Until all seats are filled, repeat the following steps:▼
##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.
## 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.
## For each of these two frontrunners, order the ballots from highest to lowest original score, and find the candidate'stheir "constituentthreshold score": theirthe originalhighest score onsuch thethat there ballotare one Droop quota (of max remaining score)voter frompower theof top.ballots Whicheverwhich frontrunnergive hasthem the higher constituentthat score getsor a seathigher.
###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.
### If there is a tie, 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)
## Exhaust one Droop quota of max remaining score.
### All ballots which (originally) scored the winner higher than their constituentthreshold score are fully exhausted (That is, their max remaining scorevoting power becomes 0, thus all their remaining scores also become 0; they can no longer affect outcomes from now on.).
### 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 max remaining score on the ballot. 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).
 
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Note that this partial exhaustion procedure 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).
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