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

[Kristofer Munsterhjelm]

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.

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

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.

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.

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.

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).

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.

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