[EM] Why I Prefer IRV to Condorcet

[Kristofer Munsterhjelm]

Juho Laatu wrote:
> --- On Sun, 23/11/08, Kristofer Munsterhjelm <km-elmet at broadpark.no>
> wrote:
> 
>> Regarding number two, simple Condorcet methods exist. 
>> Borda-elimination (Nanson or Raynaud) is Condorcet. Minmax is quite
>> simple, and everybody who's dealt with sports knows Copeland (with
>> Minmax tiebreaks). I'll partially grant this, though, since the
>> good methods are complex
> 
> Minmax is both simple and good. I think at least minmax(margins) is a
> good solution for many needs.
> 
> The weakest spot of minmax(margins) could be that it fails mutual
> majority. That means for example that nominating a set of clones
> instead of just one candidate could lead (at least in theory) to not
> winning the election.
> 
> On the other hand other methods than minmax(margins) may not respect
> the good idea of mmm to elect the candidate that has the least
> incentive among voters to be changed to some other of the candidates.

I think Schulze said that his method was the one that agreed most with 
Minmax while still being cloneproof. According to Warren, that is true 
(he refers to simulations made by Petry and Heitzig) - see 
http://rangevoting.org/SchulzeExplan.html .

At the other end of "generalizable methods" you have Kemeny. Kemeny is 
not cloneproof (it suffers from crowding). I wonder what "Cloneproof 
Kemeny" would look like, but there have been attempts to move Ranked 
Pairs closer to Kemeny. See Heitzig's Short Ranked Pairs: 
http://listas.apesol.org/pipermail/election-methods-electorama.com/2004-November/014208.html

> (Minmax(margins) fails also Smith and Condorcet loser, but those
> violations can be explained to be intentional and positive.)

That's a problem, in my opinion. A voting method also is a metric of who 
deserves to win. In that point of view, if the metric says that 
Condorcet winners are good, but the method can elect Conorcet losers, 
the metric is self-contradictory. As for Smith, I would like to have 
that as well, since if the method says Condorcet for a candidate, it 
should also say Condorcet for a set (unless there's some overriding 
strategy-proofing reason as to why not).

>> , but I'll ask whether you think MAM (Ranked Pairs(wv)) is too 
>> complex. In MAM, you take all the pairwise contests, sort by 
>> strength, and affirm down the list unless you would contradict an
>> earlier affirmed contest. This method is cloneproof, monotonic,
>> etc...
>> 
>> Perhaps you could explain it in that "say A won. B's supporters are
>> going to say "but some people preferred B to A!". Then you can say,
>> but more people preferred C to B and A to C". I'm not sure, there 
>> may be better explanations.
> 
> Also minmax(margins) is close to this. It has a very natural
> explanation. (I gave one rough explanation above. Another one is
> "elect the candidate that needs least additional votes to win all
> others".)

Kemeny is also quite simple, I suppose. It's merely "Find the ordering 
where most people agree with the preferences". However, it's not in 
polytime; finding the winner, asymptotically, is very hard (though 
linear programming tricks can be used, that makes the method extremely 
complex). I don't think Kemeny is Smith, either.

> I don't claim that Minmax(margins) would be the best Condorcet method
> for all needs. I rather claim that there are many kind of elections
> and there are many alternative targets. Minmax (margins) emphasizes
> small opposition (in favour of any other single candidate) against
> the elected candidate.
> 
> This justification focuses on the performance with sincere votes.
> Also other good criteria that describe which candidate would be the
> best may be used..
> 
> Another direction is to look for a method that is most resistent to
> straegic voting. (Many of the best known criteria emphasize this
> viewpoint.)
> 
> If the environment where the method will be used in plagued with
> widespread strategic voting then it makes sense to emphasize the
> "strategy free" oriented criteria a bit. If the voters are expected
> to be predominantly sincere then one has the luxury to focus on
> criteria that aim at electing the best winner.

The problem is that we don't know how strategic people, or parties are 
going to be. This depends on the nation and people; when New York 
briefly had STV, the parties almost immediately turned to vote 
management, but other countries with STV have been free of vote 
management. I think Ireland is one of the latter.

One way to deal with this is to make the method maximally safe against 
strategy. However, for some types of strategy this makes the method 
return worse results were the voters honest. Say there's an election 
where the "unaugmented winner" is X. If the method is strategy-hardened, 
the winner will be Y instead. Then there may be an instance in which 
people truly wanted X, but also another instance where the people truly 
wanted Y but some employed strategy. The method can't read people's 
minds and thus can't know which is the case, which means that any case 
of the former would lead to a worse result if the method was 
strategy-hardened.

Benham's Dominant Mutual Quarter Burial Resistance example comes to mind:

26: A>B
25: C>A
49: B>C  (sincere is B>A or B)

If these ballots were sincere, one would expect B to win (and almost all 
methods elect B). However, if it's true that the 49 voters are on a 
burial spree, then it would be a bad thing to elect B. But the method 
can't tell which is the case from the ballots alone.

In that sense, some strategy hardening is more expensive than others. If 
the hardening only involves ballot situations that would very rarely 
appear honestly, or if the candidate it elects to deter strategy is only 
slightly worse than that it would otherwise elect, then the hardening is 
"cheap". Otherwise, it's expensive. Some strategy hardening is next to 
free, I think; cases where the strategy applies *because* the method is 
bad at picking honest winners, not because it's good.

> There are thus different kind of environments and different kind of
> needs. One should pick the best method for each need and environment.
> Somewhere it may be e.g. FPTP or minmax(margins), somewhere something
> else.

Given the above, that's right. I can't quite see the situation where 
FPTP would be preferred, except possibly where there are only ever two 
choices (but most methods reduce to FPTP in that case).

Even though I've said it before, I'll repeat my runoff idea: to have two 
different methods, one very resistant to strategy, and another good at 
finding honest winners, and picking the winners from each for the 
runoff. It would be extremely complex, though (I remember one reply 
saying to the effect of "You can't be serious!"). It could also, 
perhaps, tempt the population to vote more strategically since "less is 
on the line", as I talked about in my message about TTR.