[EM] Why I Prefer IRV to Condorcet

[Kristofer Munsterhjelm]

Juho Laatu wrote:
> --- 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.
>> 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.

Yes; so we can say it's the method that agrees most with Minmax while 
being cloneproof and Smith.

>> 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.)

I'm not sure about this. The alternate description of Minmax as making 
use of successive eliminations may point at it involving long paths. At 
least I think that's partly the reason Schulze is so similar to Minmax 
(or Smith//Minmax).

>>> (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.

The problem is criterion compliance. Isolated, I think passing Condorcet 
and failing Condorcet loser is a contradiction, because this means you 
can possibly reverse the election and get a "worst" that is the "best". 
I know that there are weaknesses to my argument (since others could make 
the same reasoning about Consistency, for instance, and exclude all 
Condorcet methods), but I think that inasfar as voting methods are 
metrics of winners, and the reason for why one is supposed to use this 
method is because of its criterion compliance (which is really a way of 
saying certain ways of picking winners/not picking winners is 
desirable), one should take the reason to its full extent, which a 
method that fails Condorcet loser doesn't do.

>> 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.

If that is true, one should advocate Minmax on that the Minmax 
philosophy is a good one, and if it meets Condorcet, that's a bonus as 
well, but that it's the Minmax philosophy that is paramount.

Smith isn't just a hardening criterion. In a sense, it also assures 
voters that they can vote in a way they want without having to 
compensate in order to get a candidate from the Smith (or mutual 
majority, etc) set, if all other voters are honest. In this way, it 
would be similar to independence of clones: a cloneproof method tells 
voters that now it matters much less whether candidates are loosely 
spread or tightly clumped around an area, even if the candidates were 
clumped/spread apart simply because of the political environment (and 
through no adverse intent nor strategic nomination).

>>> 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.

If the concept of a social ordering is to have any use, I think the 
winner must be first on it. It could be otherwise if there was a 
splitting effect (like the PR "0.5 for single winner, 0.25 and 0.75 for 
two winners" case), but I can't quite see how that would be the case.

> 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.

That may be true; even a method like Bucklin seemed to support a 
somewhat competitive environment (at least to the extent that one of the 
candidates who didn't win were strong enough to go to court about it). 
But we don't really know; while we can program our computers to make 
millions of ballot simulations, we can't simulate the voters. All we 
have to go on, as such, is the ballot data (which can be warped by 
strategic incentive) and observations like yours.

Say we were going to make a "Organization for Condorcet Voting". 
Advocating multiple Condorcet methods would probably "split the vote" as 
it were (considering the usual state of things as Plurality). That's 
what some IRV supporters say about Condorcet itself (to my knowledge), 
that we should support IRV and then possibly go to Condorcet later 
rather than fragment electoral reform. So which will it be? What we have 
to go on is, on one hand, the theoretical measures, and on the other, a 
few pieces of data. It's not going to be easy...

>> 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).

What do you mean by that the you can get the same matrix from ballots 
with and without clones? I assume you mean something like that if you 
have a ballot specifying A1>A2>A3>B, you can derive the A*>B preference 
as it would have been even without A2 and A3. That's true. But consider 
a very simple method that just looks for clones and removes them; that 
would remove only the clones (although it would be extremely brittle and 
hence not very useful). Could such a method be implemented on matrices 
alone? If all clones are in the same direction, then yes.. I'm not sure 
about the case where they're in random order, though. Perhaps you're 
right, or maybe you can detect clones in random order as well; perhaps 
something like "if for all A in some subset, for all others B, either 
A>B or B>A with the exact same number of voters, then that subset 
consists 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).

I agree. About the only ways I can think of this happening for a public 
election would be through vote management or through extreme incentives 
to bury (on the order of FPTP's incentive to vote for frontrunners). I 
think Benham's point was to have an example where one could say 
something to the effect of "if the method resists this burial, then it 
resists any realistic burial as well"; or in the case of the 
Copeland-ish variant from which this was taken, "the method resists 
burial extremely well, so burial (of this kind) will be no problem anymore".

>> 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.))

This is going to be hard, for the reasons I showed earlier. But it's a 
good point: if we can get data based on real life situations, then those 
are definitely preferrable to others.

Though there's always the chance that if we were to set up an 
Organization for Condorcet Voting, IRV or FPTP supporters would say 
something like "they say IRV is nonmonotonic, well, this thing can't 
even make up its mind what the true winner should be!" (regarding 
Reversal symmetry). That's one way theoretical issues, even those that 
don't really matter in real life elections, could come into play. (Of 
course, one could then respond that "IRV squeezes the center and FPTP 
explodes said center, but Condorcet supports the center", for instance. 
I'm using general statements here - they may not fit completely, but you 
see the idea.

>> 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.

Yes, or implement them into programs that can be used for informal 
voting or voting on websites or in similar situations. I think the 
voting program mentioned here some time ago (Selectricity?) aims towards 
the latter.