On 09/15/2012 07:33 PM, Juho Laatu wrote:
I can't draw any clear conclusions from this on how good Condorcet methods are in visualizing the results or an ongoing counting process. The measure of number of voters to change the result seems to be quite natural measure of "distance to victory". Another approach to visualizing the results could be to try to point out "how good winner each candidate would be". In minmax(margins) these measures coincide (measured as additional votes). In Smith set based methods I guess the intended message is that Smith set candidates are the best winners, although that does not correlate with distance to victory (if measured as number of voters that may make someone win). Each Condorcet method has its own philosophy and measures, and probably visualization too (unless some generic / method independent visualizations are used).
The voting criterion failure finder I've referred to in my trie post does something like that to give its GA a fitness measure. In general, to turn ranking into scores, it finds the number of plumpers needed to raise a candidate one level in the rankings. These numbers give relative scores - e.g. if X is the winner, there are 1000 voters, and it takes Y 100 votes to tie X, then in some respect Y is 10% worse than X.
(More precisely, the relative scores (number of plumpers required) become terms of type score_x - score_(x+1), which, along with SUM x=1..n score_x (just the number of voters), can be used to solve for the unknowns score_1...score_n. These scores are then normalized on 0..1.)
It seems to work, but I'm not using it outside of the fitness function because I have no assurance that, say, even for a monotone method, raising A won't decrease A's score relative to the others. It might be the case that A's score will decrease even if A's rank doesn't change. Obviously, it won't work for methods that fail mono-add-plump.
Turning rankings into ratings the "proper" way highly depends on the method in question, and can get very complex. Just look at this variant of Schulze: http://arxiv.org/abs/0912.2190 .
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