[EM] percentage support
Daniel Bishop
dbishop at neo.tamu.edu
Mon May 2 19:56:59 PDT 2005
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.
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