[EM] Why I Prefer IRV to Condorcet

[Juho Laatu]

--- On Tue, 25/11/08, Kristofer Munsterhjelm <km-elmet at broadpark.no> wrote:

I'll try to answer very shortly to most of the points.
I can comment more if there are some interesting ones.

> From: Kristofer Munsterhjelm <km-elmet at broadpark.no>
> Subject: Re: [EM] Why I Prefer IRV to Condorcet
> To: juho4880 at yahoo.co.uk
> Cc: election-methods at electorama.com
> Date: Tuesday, 25 November, 2008, 1:37 PM
> 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 .

The claim seems to be about Smith//MinMax.

> 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

Note that the minmax philosophy is to study paths of
length one. Minmax philosophy says that voter interest
to replace the elected candidate with another is more
relevant than their interest to replace the candidates
in chain. (Such chains of changes do not typically
happen in real life after the election.)

> > (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.

Yes if one sets that as a target. The alternative is
to emphasize also other aspects like being free of
strategic voting related risks. I think minmax can be
seen as an ideal definition (for some needs) of which
candidate is best.

> 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.

Minmax may elect the Condorcet loser only when there
is no Condorcet winner. And only in situations where
all other candidates are worse than the Condorcet
loser from the minmax philosophy/utility point of view.

> 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).

I don't see that as a requirement even if there were
no strategy-proofing needs. The minmax philosophy says
that voters may have more interest to replace the
elected Smith set member with another member of the
set than they have interest to replace someone outside
of that set with others.

> >> , 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".

One could see Kemeny as a good definition of a good
social ordering. That may or may not correlate with
the definition of the best single winner.

> 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.

Yes. One has to guess, or one may modify the system when
one sees the level of strategic voting and its level of
impact. In general I believe strategic voting would not
be as bad as discussions on this list might suggest.
Take for example all the numerous Top Two Runoff
elections today. People speculate on strategic
possibilities and other problems only afterwards but
in most cases they vote sincerely in the elections.

> 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.

Yes, there is always a trade-off. Maybe it is a worse
failure to elect a wrong winner due to a successful
strategic plot than due to a method that doesn't
always elect the best winner. But failure to elect
the best possible winner with sincere votes is a
serious problem too.

One observation about clones. One can get the same
pairwise matrix from ballots that contain clones and
from ballots that do not contain clones. That means
that (matrix based) clone proof methods will protect
also other sets of candidates than sets of clones
(e.g. Smith set may or may not consist of clones).

> 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.

Yes. I hope that Condorcet elections would have
relatively few strategic voters, and that their
impact would be just noise. If there are large
numbers of strategic voters (e.g. 49%) then the
system has pretty much already failed (except if
it is the intention of the method that all should
vote strategically).

> 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.

I'd like to see all the vulnerability reports
and hardening plans to be accompanied with some
analysis and/or example cases where one tries
to estimate the seriousness of the problem
against expected real life situations. Pure
theoretical examples are not good enough for
practical real life decisions.

Let me take one example. Minmax indeed may elect
Condorcet losers. But is this probable in real
life elections? I think the probability is very
very small. So, the threat is there but it has
no importance in real life elections. ((In
addition one could of course also claim that if
minmax elects a Condorcet loser it does so for
a good reason.))

> > 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).

I reserved some space for interest to intentionally
base the society on a two-party model. That can be
seen as one form of democracy that does indeed work.
I'm not really a strong proponent of it but I can
understand if someone finds it to be a working
system. It has also some claimed benefits like strong
governments when compared to typical multi-party systems.

> 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.

Yes, at least in theory this makes sense. In the
26-25-49 example above and with some basic Condorcet
method and IRV (with same strategic or sincere
ballots) you would elect the Condorcet winner despite
of the strategy. (It is enough to get the Condorcet
winner to the runoff from either method.)

> 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.

Yes, that is possible too. But as already said, I'd
expect many societies to lean towards strategy free
voting. And many strategies are also quite difficult
to implement in real life elections (in most societies).

One should maybe start testing different methods (that
elect good winners but that are not necessarily
maximally rigged to defend against strategies) in some
smaller elections to first gain trust that the
strategies will not be a serious problem.

Juho