Reweighted range voting

Reweighted Score Voting, also known as Reweighted Range Voting (RRV), is a Multi-Member Score voting System. It is the natural extension of the Jefferson Method to Multi-Member System. If two level score (ie Approval voting) ballots are used along side the D'Hondt reweighting variant, then it reduces to Sequential Proportional Approval Voting.

Procedure

Each voter submits a ballot which, for each candidate, indicates a numeric score which is less than or equal to some maximum number MAX.

Each ballot is given an initial "weight" of 1.

1. The highest scoring candidate wins the first seat.

2. When a candidate wins, all ballots supporting that candidate are then reweighted, resulting in reduced vote weight going forward for voters who have successfully helped to elect a candidate. This reweighting happens in proportion to the amount of support given in order to ensure that all voters have an equitable amount of influence on the election

Reweighted ballot = 1/(1+SUM/MAX), where SUM is the sum of the scores that ballot gives to the winners-so-far

3. The remaining candidate with the highest total reweighted score wins, and the process is repeated until all available seats have been filled.

See http://www.rangevoting.org/RRV.html for more details (some of the wording on this page is taken from there). A variant is to use the reweighting formula 0.5/(0.5 + SUM/MAX).

Reweighting Variations

One variation is to use the reweighting formula 1/(1 + SUM/MAX). This variant reduces to D'Hondt when voters vote on party lines.

Another variant is to use the reweighting formula 0.5/(0.5 + SUM/MAX), or equivalently, 1/(1 + 2*SUM/MAX). This variant reduces to Sainte-Laguë when voters vote on party lines.

There is an infinite number of variants that all use the fallowing formula: K/(K + SUM/MAX) where ½≤K≤1. The two above formulas are special cases for when K equals 1 and ½.

Method Variations

A 5 STAR variation in which a final runoff is performed for the last seat available has been proposed in order to incentivize voters to more honestly express their preference order and degree of support.

Each voter submits a ballot in which candidates are scored from 0 (worst) to 5 (best.)

Each ballot is given an initial "weight" of 1.

1. The highest scoring candidate wins the first seat.

2. When a candidate wins, all ballots supporting that candidate are then reweighted, resulting in reduced vote weight going forward for voters who have successfully helped to elect a candidate. This reweighting happens in proportion to the amount of support given in order to ensure that all voters have an equitable amount of influence on the election

Reweighted ballot = 1/(1+2*SUM/5), where SUM is the sum of the scores that ballot gives to the winners-so-far

3. The remaining candidate with the highest total reweighted score wins each seat available- up until the final seat up for election.

4. For the final seat available, the two highest scoring candidates remaining runoff, with the candidate preferred (scored higher) by more reweighted ballots winning the final seat.