Score Remainder Voting

[Brian Langstraat]

Score Remainder Voting (SRV) is a voting system for multiple winners similar to Reweighted Range Voting (RRV) (http://www.rangevoting.org/RRV.html) except votes retain power equal to the remainder of their contribution beyond the winning threshold for each winner.

1. Voters give a score within a range (0-99, blanks=0) to each candidate on the ballot.

2. Scores are summed to calculate the score totals for each candidate.

3. The winning threshold = overall score total / number of remaining winner(s).

[Example: Winning threshold = 1,000 voters * 90 / 5 remaining winners = 18000 score total]

4. If no candidates have score totals that exceed the winning threshold, then the scores are ignored (until a winner is determined) for the candidate with the lowest score total.

5. Steps 2,3, and 4 are repeated until at least one candidate exceeds the winning threshold.

6. The candidate with the highest score total (that exceeds the winning threshold) wins.

7. The remainder retained by each vote equals:

[Maximum possible vote] - [Vote score] * [Winning threshold] / [Winner score total]

This remainder retained by each vote becomes the new maximum possible vote (for each voter).

8. Steps 2 through 7 are repeated until the winner(s) are determined.

[Brian Langstraat]

To clarify, the initial maximum possible vote equals the maximum of the range.

Examples are attached that compare Score Remainder Voting (SRV) to the imperfections in Reweighted Range Voting (RRV) (http://www.rangevoting.org/RRV.html):

SRV_1:

In the first round, the totals are Z=7070, X=7050, and Q=6110, so RRV elects Z. That deweights X and Q so that, second round, X wins. (The second round totals are X=5167, and Q=4132.)

SRV_2:

Now you (an extra voter) come with a vote Q>X>Z, for example Q=99, X=77, Z=0.

That makes X win the first round. (First round totals: X=7127, Z=7070, and Q=6209.) That win  deweights Z and (heavily) Q, allowing Z to win the second round. (Second round totals: Z=5065.8, Q=4211.2.)

Summary of situation:

Before you vote: Z & X win.

After your Q>X>Z vote: X & Z win.

Q had too low of a score total for your extra vote to make a difference; at least X was the first winner.

The multi-winner "participation property" passes in this example.

SRV_3:

A neat property of SRV is that every vote has power up to the maximum range value. 

Note in SRV_1 that summing each threshold and the unused remainder equals the number of votes times the maximum range value.

If every candidate is a winner and every voter gives a non-zero score to every candidate with a few high scores for their favorites, then every voter's voting power will be used entirely.

Note that adding a score of 1 under Q results in 0 unused remainder.

Perhaps, a range like 0-99 would not force voters to use their full voting power, but a 5-star (1-5, empty=1) would essentially force voters to use their full voting power.

[Brian Langstraat]

There is a change to the winning threshold calculation in Score Remainder Voting (SRV) to the Droop Quota which is fairer to the early winners:

New Description:

1. Voters give a score within a range (0-99, blanks=0) to each candidate on the ballot.

2. Scores are summed to calculate the score totals for each candidate.

3. The winning threshold = Floor of [Number of voters] * [Maximum of the range] / [Number of winner(s) +1] + 1.

[Example: Winning threshold = 1,000 voters * 99 / (4 winners +1) + 1 = 19801 score total]

5. The candidate with the highest score total wins (even without reaching the winning threshold).

6. The remainder retained by each vote equals:

[Maximum possible vote] - [Vote score] * [Winning threshold] / [Winner score total]

If a candidate wins without reaching the winning threshold, then at least one vote will have a negative remainder that will be used in the next round(s).

This remainder retained by each vote becomes the new maximum possible vote (for each voter).

7. Steps 5 through 6 are repeated until the winner(s) are determined.

Using the Droop Quota may result in "score debt" for some winning votes in elections with many candidates and few winners.

It would be risky to use a "score debt" strategy to effectively harm an opponent, since acquiring a "score debt" would require voting a high score for a winning candidate that does not cross the winning threshold and voting for a losing rival that does not cross the winning threshold.

"SRV_2" Example Update:

Now you (an extra voter) come with a vote Q>X>Z, for example Q=99, X=77, Z=0.

That makes X win the first round. (First round totals: X=7127, Z=7070, and Q=6209.) That win  deweights Z and Q, allowing Q to barely win the second round. (Second round totals: Q=5726.3, Z=5698.7.)

Summary of situation:

Before you vote: Z & X win.

After your Q>X>Z vote: X & Q win.

The multi-winner "participation property" passes in this example.

[Jeremy Macaluso]

I don't think that this solves the problems that you want it to solve, and think that it might cause more issues, depending on how the retained remainder changes the second time. Can you walk through each step of each loop for a simple single-issue election? It has 10 candidates running for 5 positions, with 5 on each side of the issue, and voters with a 60/40 split voting precisely on party lines.

Candidates a-j, 5 winners
60 votes: a-e maximum, f-j minimum
40 votes: a-e minimum, f-j maximum

In this I would expect candidates a,b,c,f,g to win.

[Brian Langstraat]

Jeremy,

The attached SRV_6 is a picture from a crude spreadsheet that I am using to experiment with SRV.

For the max and min values, I cheated slightly so there would not be ties.

The win order is a, b, f, c, g.

The winning threshold = [100] * [99] / [5 +1] + 1 = 1651

The remainder retained by the first "60" vote = [99] - [99] * [1651] / [6140] = 72.4

Note how summing the thresholds and final remainders = 5 * 1651 + 892.5 + 752.5 = 9900

[Brian Langstraat]

An example of Approval Remainder Voting (ARV) is attached, SRV_7.

For ties, I chose the first alphabetically.

The win order is a, b, f, c, g.

The winning threshold = Floor of [100] * [1] / [5 +1] + 1 = 17

The remainder retained by the first "60" vote = [1] - [1] * [17] / [60] = 0.72

Note how summing the thresholds and final remainders = 5 * 17 + 9 + 6 = 100

[Brian Langstraat]

Again, there is a change to the winning threshold calculation in Score Remainder Voting (SRV) to use the highest score given by each voter which removes the use of "score debt":

New Description:

1. Voters give a score within a range (0-99, blanks=0) to each candidate on the ballot.

2. Scores are summed to calculate the score totals for each candidate.

3. The winning threshold = Floor of [Sum of highest score given by each voter] / [Number of winner(s)].

5. The candidate with the highest score total wins (even without reaching the winning threshold).

6. The remainder retained by each vote equals:

[Maximum possible vote] - [Vote score] * [Winning threshold] / [Winner score total]

This remainder retained by each vote becomes the new maximum possible vote (for each voter).

7. Steps 5 through 6 are repeated until the winner(s) are determined.

In the final round when a candidate wins without reaching the winning threshold, at least one vote will have a negative remainder.

These negative remainders are not used in further rounds to determine winner(s).

The votes with positive and negative remainders sum to 0, which seems like SRV is similar to a voting regression function.

"SRV_2" Example Update:

Now you (an extra voter) come with a vote Q>X>Z, for example Q=99, X=77, Z=0.

That makes X win the first round. (First round totals: X=7127, Z=7070, and Q=6209.) That win  deweights Z and Q, allowing Z to barely win the second round. (Second round totals: Z=5013.5, Z=4086.)

Summary of situation:

Before you vote: Z & X win.

After your Q>X>Z vote: X & Z win.

Q had too low of a score total for your extra vote to make a difference; at least X was the first winner.

The multi-winner "participation property" passes in this example.

[Mark Frohnmayer]

It's confusing to see SRV attached to something that isn't Score Runoff Voting. I suggest you pick a new moniker.

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[Brian Langstraat]

Mark,

I noticed that Score Remainder Voting (SRV) and Score Runoff Voting (SRV) have the same acronyms which is pretty common with these sets of letters.

Perhaps, a better moniker could be Score Correlation Voting (SCV).

What are your thoughts on Score Remainder/Correlation Voting?

How does it compare to RRV and SRV-PR?