Curt Siffert wrote:
I know many of us are here to work on the best method for various social choice purposes. But many of us are specifically interested in political elections.
And there's a problem with this. Plurality actually serves two purposes. It is a bad way to select a winner, but it is also a way to track percentage support over a period of time, and by determining proportional support when it's relevant.
Democratic primaries are an example. The proportion of votes a candidate receives determines how many delegates they receive. But even if that particular decision structure is done away with, there are plenty of other reasons to track proportional support - polling, for instance.
There's nothing preventing you from conducting a Plurality poll for a Condorcet election. Except perhaps for the discouragement of knowing that such a poll would lose its usefulness in predicting the winner.
And this is something that Condorcet methods cannot do. You cannot derive, from a Condorcet ballot collection, how much percentage support each candidate got. You can't give each candidate a share of 100% in a way that all candidates would agree on. If you can, I'd love to know how.
Here's a method I tried a few months ago:
Start by determining the number of additional "bullet votes" each candidate would need in order to win or tie.
For example, suppose you polled 7 people for an {A, B, C, D} election, and:
* D is the winner
* A would win with the additional ballots 4:A
* B would tie D with the additional ballots 3:B
* C would win with the additional ballots 6:CLet x be the "support" for the winner. The "support" for the remaining candidates can be expressed in terms of "votes behind the winner".
A: x-4 B: x-3 C: x-6 D: x Total: 4x-13
Next, find x such that the total "support" is equal to the number of voters. In this example, x=5.
A: 1 B: 2 C: -1 D: 5
Finally, divide by the number of voters, in order to get each candidate's support as a percentage.
A: 14% B: 29% C: -14% D: 71%
I rejected the idea because I didn't like having to explain what negative support means, but maybe someone can think of a way to fix this.
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