[EM] 3 or more choices - Condorcet

[Kristofer Munsterhjelm]

On 10/05/2012 12:12 AM, Juho Laatu wrote:
>> And even in the three-categories classification, it's hard to find
>> any objectively "best" method.
>
>
> The third category was "quality of the outcome under honesty". For
> this category only, finding the best method is straight forward in
> the sense that one can freely decide what the criterion of the best
> candidate is in each election.

The third category is both easy and hard. It's easy in that if you know 
what society wants, the answer presents itself readily (unless the 
desideratum is very indirect or statistical). It's hard in that you have 
to know what's best. Is an utilitarian approach best? Sum-of-utilities? 
Mean-utilities? Is equality and fairness valued in itself, thus possibly 
leading to a preference for candidates everybody thinks is "good enough" 
in favor of those some love and some hate? Or is utility hidden or 
incommensurable to begin with? Perhaps the best one can do is make a 
hindsight prediction based on foresight data, like in the OD_Ranking 
link I gave. In any event, there's no "out of nothing" way to find the 
correct metric, I think.

> The second category was "resistance to noise and strategy". It is
> difficult to estimate how much protection there should be against
> each threat scenario. It is easier to find the correct answers after
> the method has been in use for a while (in the given environment).

If you (the election method implementer) only get one shot, that makes 
it more difficult still, because it would generally be advantageous to 
err on the side of caution so that arguments similar to those against 
IRV don't get used against your method, or so that the method doesn't 
perpetuate two-party rule (which you won't know until the method is 
actually used); but assuming you're on the Pareto front, each hardening 
within this category will lead to a weakening of the other two.

> The first ctegory was "consistency with itself". Maybe this can be
> measured somehow, although opinions on what is good may be
> subjective.

Yes. Say you have to decide between margins and wv for the Ranked Pairs 
rule. Let's disregard strategy susceptibility for now for the sake of 
illustrating the point. Then the wv version passes Plurality while the 
margins version passes symmetric completion. Which do you want? I can't 
see pure reasoning finding the answer to that. Rather, it would appear 
to be a matter of societal preference. (IMHO, Plurality seems to be more 
"serious" than symmetric completion, but then I do prefer wv.)

> Summing up all three properties to determine which system is best
> could be done in theory, but is of course quite complex.

Hence my reference to Pareto fronts. It's conservative - retaining lots 
of methods that could be excluded if we knew how to compare the category 
elements - but seems to be the best we can do without actually knowing 
how to compare.

> I guess the most discussed topic around comparison methods has been
> strategy resistance (category two). Many of the comparison methods
> are so simple that category one doesn't cause major problems. In
> category three there might be something more to discuss. Also soft /
> heuristic approaches could be valid (in addition to the traditional
> simple and hard ones (that may be easier to define and agree)).

Green-Armytage's paper on Condorcet-IRV hybrids is a little more "soft" 
in category two. He determines how often strategy (of any kind) works 
for the voters engaged in the strategy, instead of grouping it into 
offensive truncation/equal-ranking/whatever. He also does the same with 
candidate entry and exit instead of saying clone-proof vs non-clone-proof.

Soft approaches would depend on the probability distribution of the 
votes, also. Impartial culture is not very realistic.