[EM] 3 or more choices - Condorcet

[Juho Laatu]

On 6.10.2012, at 0.03, Kristofer Munsterhjelm wrote:

> 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.

Yes, one always has to understand the needs and make the decision based on those needs. There are for example the two classical categories, ranked/majority and rated/utility based categories. And then, wide support vs. first preference support etc.

Maybe third category definitions may include already some well established strategic concerns in the sense that even though one would think that some utility/ratings based function would be ideal, one uses a majority based function because one thinks that majority is the way to rule competitive societies anyway (since opposition that has majority would be too difficult or too unfair to suppress). But I guess this is still a sincere definition of who should win with sincere votes.

> 
>> 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.)

In this category we are really talking about personal preferences. There are many criteria that can be used to point out paradoxes (that may also violate the chosen third category rule). All methods have some paradoxes and therefore it may be just a question of good positive and negative marketing which method gets the most negative points from the audience in the first category. Both plurality and symmetric completion could be used. I guess one could also reject all Condorcet methods since the possibility of cyclic opinions in the results is unpleasant to many. (Woodall says that all methods should meet Plurality but I don't see Plurality as a requirement, not even for majority methods.)

If we first decide what third category rule to use and what second category adjustments are needed to make the method work well, then what do the remaining first category decisions look like? Do they work against the chosen third and second category approaches? Do they make the method better? Or do they make the method better in the eyes of the audience? Maybe we could choose which one of the otherwise equally good methods we would use. Or maybe first category would tell us which methods are politically possible (not too much confusion or opposition).

> 
>> 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.

There are many approaches to making the decisions. Here's one classification that I often use. 1) Black and white compliance to a set of exact criteria. 2) Statistical / simulated probabilities based on some model of the society and voter behaviour. 3) Practical analysis of the dynamics of different threat scenarios in the given society. I tend to think that the third class is the one that should be used to make the decisions. The other two classes are to be used as tools when making the decisons, but their results should be filtered through 3. Class 1 is just definitions that typically aim at something positive but that may distort the end result by being too black and white in one direction or another. (Your three categories apply also here.) My main point here was anyway just that the third class above is so compelx that it often introduces some softness to the decisions.

Juho


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