On 16.9.2012, at 9.57, Kristofer Munsterhjelm wrote:
> 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.
Ok, that seems to follow the minmax(margins) philosophy. In visualizations the
performance or quality of each candidate could well be indicated with "%" as
you do (e.g. "10% less" or "90% of").
If there is a top loop, then one can measure either distance to the winner or
distance to an imaginary Condorcet winner. The winner would thus be said to be
either "100% good" or only "99% good" (= 1% distance to being a Condorcet
winner).
>
> (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.
What should "candidate's score" indicate in single-winner methods? In
single-winner methods the ranking of other candidates than the winner is
voluntary. You could in principle pick any measure that you want ("distance to
victory" or "quality of the candidate" or something else). But of course most
methods do provide also a ranking as a byproduct (in addition to naming the
winner). That ranking tends to follow the same philosophy as the philosophy in
selecting the winner. As already noted, the mono-add-plump philosophy is close
to the minmax(margins) philosophy, also with respect to ranking the other
candidates.
I note that some methods like Kemeny seem to produce the winner as a byproduct
of finding the optimal ranking. Also expression "breaking a loop" refers to an
interest to make the potentially cyclic socielty preferences linear by force.
In principle that is of course unnecessary. The opinions are cyclic, and could
be left as they are. That does not however rule out the option of giving the
candidates scores that indicate some order of preference (that may not be the
preference order of the society).
>
> 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 .
They seem to aim at respecting multiple criteria. Many such criteria could
maybe be used as a basis for scoring the canidates. Already their first key
criterion, the Condorcet-Smith principle is in conflict with the mono-add-plump
score (there can be candidates with low mono-add-plump score outside the Smith
set).
My favourite approach to scoring and picking the winner is not to have a
discrete set of criteria (that we try to respect, and violate some other
criteria when doing so) but to pick one philosophy that determines who is the
best winner, and also how good winners the other candidates would be. The
chosen philosophy determines also the primary scoring approach, but does not
exclude having also other scorings for other purposes (e.g. if the "ease of
winning" differs from the "quality of the candidate").
Juho
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