Top quota methods
What if we could sequentially take the biggest chunk of support for a candidate over a quota of voters?
Think of a voronoi cell. There is a perfect condorcet winner for each cell. However, we only have so many seats. So we can sort voters by how much they like the candidate for each candidate and add up support over however many voters are needed for a seat.
We would elect the candidate with the biggest support over a quota of voters and then consider the remaining voters. There are many options for measuring support:
- sum of scores
- minimax: smallest pairwise win
- schulze: strongest beatpath
We could use any voting method really, but I think we need a way to sort voters so we can add them one at a time starting with the most supportive. It's easy to see how a voter's support contributes to a sum. It's a little harder to see how a vote contributes to the smallest pairwise win. It's harder still to see contribution to a strongest beatpath.
Back to the motivation - The benefit is no vote splitting.
Also, we could do better by some optimization, which could either be realistic or not, instead of sequential selection.
@paretoman I’m actually not sure I understand precisely what you mean. Could you elaborate more with a small example?
Here's a simple example to show proportionality. This example works the same no matter what the measure of support. Basically, all these measures are clones of STV but without vote splitting. The measures I'm talking about are score, smallest pairwise win, and strongest beatpath. Also, I should say that I don't really know if the measures would work for sorting.
2 parties: A, B.
quota: 50 voters.
The votes are A 55, B 45.
The best quotas of 50 voters give A 50 and B 45.
A gets a seat. The quota of 50 A-voters are removed.
Now we count the remaining voters, A 5, B 45.
B gets a seat.