User:Jameson Quinn/SPARTA voting: Difference between revisions

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Jameson Quinn

Autopatrolled users, Bureaucrats, Confirmed users

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Revision as of 15:40, 30 October 2020 (view source) Jameson Quinn (talk \| contribs) (Renaming variables for clarity) Tag: Visual edit ← Older edit		Latest revision as of 21:09, 12 November 2020 (view source) Jameson Quinn (talk \| contribs) (cats)
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Line 2: # 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. # Until all seats are filled, repeat the following steps: ## ~~Using the current ballots and their weights, find~~Find the two "frontrunners", the candidates with the highest total "remaining scores". ## 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. ###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. ### 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)▼ ####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). ## Exhaust one Droop quota of ballots.▼ ##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. ### All ballots which score the winner higher than their constituent score are fully exhausted.▼ ###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 (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) ▲## Exhaust one Droop quota of ~~ballots~~remaining score. ▲### All ballots which ~~score~~(originally) scored the winner higher than their ~~constituent~~threshold 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.~~of ~~Use this to calculate the new maximum~~remaining score ~~on the ballot~~overall. ~~If the previous maximum score on the ballot was M (to begin with, M=5), the new maximum will be M-ME~~ ####Multiply the remaining voting power of each of these ballots by (1-E). ~~####Any scores on these ballots which are higher than the maximum score is set to the maximum score.~~ 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. [[Category:Multi-winner voting methods]] [[Category:Proportional voting methods]]