[EM] percentage support

[Daniel Bishop]

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:C

Let 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.