[EM] Strong methods (was Re: 3 or more choices - Condorcet)

[Juho Laatu]

On 30.9.2012, at 11.56, Kristofer Munsterhjelm wrote:

> On 09/29/2012 10:49 PM, Juho Laatu wrote:
>> What is a "strong" Condorcet method?
> 
> Basically, one that gives good results while being resistant to tinkering by the parties (who have greater capacity to coordinate strategy than do the voters, and more to lose under the new regime), and not giving weird results or having weird result dynamics that could be used to discredit the method.

That's a prestty good definition of "good". I'd say good results (there may be different definitions) with sincere votes, and (if needed) good behaviour in the presence of strategists too.

> 
> In practice, that means: is cloneproof, passes independence of as much as possible (independence of Smith-dominated alternatives, say), and is monotone.

These criteria could be one set of definitions of a good (sincere) winner. I usually do not assume the first two ones since there may be good (sincere) winners also outside those criteria. Monotonicity is maybe more natural in the Condorcet category.

> 
> River would be even better than Ranked Pairs, since River passes independence of Pareto-dominated alternatives and RP doesn't, but River is even less known than Ranked Pairs.
> 
> I've put strong in quote marks because I know others may disagree with my priorities. FairVote obviously doesn't consider the "having weird result dynamics" part important as long as the strangeness can't be exploited by deliberate strategy.

If one looks positively at their criteria, maybe they put strong emphasis on the marketability of the method. That marketability may include some tendency to favour the large parties.

> 
> To digress a bit, I think you could say strong methods go further in satisfying three categories than do not-as-strong methods.
> 
> The first is consistency with itself. Nonmonotone methods do badly here. The intuitive idea is that if a method is not monotone (say), then that means that its concept of what is better is lacking - it's like someone who says "I'm closer to the city" after traveling in the wrong direction. It's important to make clear that whether or not these inconsistencies can be exploited through strategy is not really important. The danger is that a perfectly innocent election will find itself on the wrong side of an inconsistency and so the result will be either inferior (as a result) or less legitimate (because people will say "WTF is going on here?").
> Of course, there are some such inconsistencies we have to accept if we want Condorcet.

Yes, it is good if the winner is someone who can be said to be the best according to some definitions, and people agree with the sensibility of those definitions. This means picking the best winner (with sincere votes), not a random winner.

> 
> The second is resistance to noise and strategy. Independence of clones fit here, as well as independence of X (Smith-dominated alternatives, Pareto-dominated alternatives, weak IIA). The resistance may protect against strategy - cloneproof methods keep parties from running an army of identical candidates - or improve the outcome when there is no strategy - e.g. by not being affected by the liberal parties' vote-splitting in a replay of the 1988 South Korean presidential election.

(I just note that independence of clones can be an interesting topic both when discussing behaviour with sincere votes and strategies.)

> 
> The third is quality of the outcome under honesty, according to some metric or desired logic. It's hard to say which metric one should pick, unfortunately, and for Ranked Pairs (and Schulze), there's probably no simple metric that the method optimizes. Furthermore, the logic one uses for rated methods probably wouldn't directly fit onto rank methods (because utilities are either unknown or not applicable).

It seems that I assumed above that this category and the first category are related. Maybe this category implies also the first category. I.e. there is no such good logic of what we desire that would break against the first caregory. (Or maybe, if we step outside the Condorcet domain and think about IRV, then maybe the idea of kicking the weakest candidate out at every round makes sense in some setup??)

> 
> I'm not sure where Condorcet compliance fits into the categories above, either. Perhaps it's the third, in a sort of deontological logic that says "do whatever you want, but if there's a candidate that would win every runoff, elect him". Perhaps it's a consistency criterion, where the people expect X to win outright if he can win every runoff. Or maybe it's "doing without strategy what the voters could do with enough coordination in other methods", easing the burden on those voters - or a way to have the method resist single-group repeal efforts, where electing the CW ensures that if the supporters of a loser tries to repeal or complain, there will always be a greater group of supporters to defend the method, no matter who that loser is.

I think Condorcet compliance could be included in the third category requirements. But it could be left out as well. Condorcet criterion makes sense when we want to respect the will of the majority. This is a typical approach in politics and in other competitive environments. In such environments it makes quite good sense to allow the majority to decide (based on centuries of good and bad experiences that have maybe left us with this approach, as the least harmful one :-) ). Some elections might still be based e.g. on best average utility or something like that, but in majority oriented elections Condorcet criterion seems to be a very solid basic approach.

Juho


> 
> (Well, that turned out quite a bit longer than I expected. And others might disagree.)
> 
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