[EM] Why I Prefer IRV to Condorcet

[Kristofer Munsterhjelm]

Juho Laatu wrote:
> --- On Fri, 5/12/08, Kristofer Munsterhjelm <km-elmet at broadpark.no> wrote:
> 
>> Alright. You may like Minmax for being Minmax, and
>> that's okay; but in my case, I'm not sure if it
>> would withstand strategy (there's that "hard to
>> estimate the amount of strategy that will happen"
>> again), and the Minmax heuristic itself doesn't seem
>> important enough to trade things like clone independence and
>> Smith for.
> 
> The good points in Minmax are related to behaviour
> with sincere votes. It is not really rigged to
> remove maximum number or amount of strategic threats
> (but to implement one natural sincere utility
> function). The question then is which properties one
> should emphasize (electing the right winner vs. not
> electing a wrong winner due to strategic voting).
> 
> All Condoret methods are vulnerable to some very
> basic strategies. Some Condorcet methods try to
> fix some additional threats. One may say that
> differences in the level of vulnerability are not
> that big. And fixing one problem often leads to
> vulnerability on some other area.

There is probably a Pareto front in this respect. Just like some methods 
fail more criteria than others, some methods would do both worse on 
sincere votes and resist strategy less; it would be Pareto-dominated by 
better methods. But since there's a Pareto front and not a single 
objective, some methods on that front will be better at translating 
sincere expression (whatever metric is used to measure this), while some 
are much more resistant against strategy.

If we take that further, some compliances are probably more "expensive" 
than others. Intuitively, I think clone independence is pretty 
inexpensive (that it alters situations that is much more likely to be 
due to strategy than honest voting), but I have no proof of this, of 
course; and similarly intuitively, I think that MDQBR (mutual dominant 
quarter burial resistance) would be very expensive, since so many voters 
are burying that the dishonest ballot bundle will collide with a sincere 
ballot bundle (in the latter case, the "buriers' candidate" should win, 
because there are no buriers and the expression is sincere).

> One may say that all Condorcet methods are quite
> resistant to strategic voting, espacially in the
> typical environments (large public elections with
> independent decision making and with limited
> information on how others are going to vote).

That's what it all boils down to. We don't know whether Condorcet 
methods are adequately resistant. The cover-all-bases approach is to try 
to have the method pass as many criteria as possible so that even in the 
worst case, the system resists strategy. If the criteria are cheap, 
there's little harm (except the waste of work, but having a margin of 
safety is probably a good thing, ceteris paribus). The other approach 
would be to actually investigate the kind of strategy that would 
develop, but this is difficult: even if we had access to near-unlimited 
numbers of experiments, we wouldn't know whether the dynamics would lead 
to things like vote management on one hand, or the initial strategy 
resistance would discourage people from building upon them on the other.

> I say this to present Minmax in a positive light.
> Maybe the fairness of the method is also a
> positive value. Maybe the strategic defences are
> not needed, especially since there is a risk that
> we don't elect the best winner then. Maybe focus
> on the positive properties even encourages sincere
> voting (=let's just pick the best winner). Maybe
> the Minmax viewpoint to who is best is accurate
> enough for the purpose.
> 
> And if there are meninful strategies and counter
> strategies then I think the method may already
> have failed.
> 
> Minmax is not necessarily the ideal utility
> function (for ranked votes). I think different
> elections may well have different sincere needs.
> Different methods may be used for different needs.
> In Minmax it is quite easy to justify electing
> Condorcet loser (in some very rare cases) or to
> fail strict clone compliancy (in some very rare
> cases). Also mutual majority can be explained away
> (I already tried this in this mail stream) but
> here it is easier to give space also to other
> opinions.

This raises the question: for ranked electoral methods, what is the 
ideal utility function, or more precisely, what is the ideal honest 
aggregation function? One may argue for Borda being it (Bayesian 
regret), or Minmax (gives up as little as possible), Kemeny-Young 
(maximum likelihood, maximize the number of voters that agree with each 
preference) or Dodgson (minimize ballot differences to CW). In the case 
of different ideal functions for different needs, the question is 
displaced to what conditions would make, say, Minmax, optimal.

> Some more words on trading clone independence and
> Smith. Note that Minmax doesn't trade them away
> since it respects them almost always. (And in these
> cases we can diecuss if it is justified to violate
> these criteria in these special cases.) A less than
> 100% compliance with some criteria may sometimes be
> useful. Either beneficial or acceptable because some
> criteria need to be violated in any case.

That goes both ways. If Minmax respects them almost always, then wanting 
a method that behaves maximally like Minmax except when doing so would 
make it vulnerable to cloning (or non-Smith, or whatever), trades off 
little for a large "margin of safety" gain, since the situations are 
rare. Of course, the other way is what you mentioned, that if they are 
rare situations, then there may not be a point in making the method more 
complex just to cover them. (Then again, one should note that in the 
face of an adversary, corner cases will occur more often than usual, 
since the adversary will actively seek them out if they benefit it.)

> I did'n btw quite like term "Minmax heuristic" since
> my dictionary defines heuristic in mathematics,
> science and philosophy as "using or obtained by
> exploration of possibilities rather than by
> following set rules". The rules and justifyig
> explanations of Minmax(margins) are very exact.
> (Actually most other Condorcet methods are more
> inclined towards heuristic style exploration, e.g.
> to find the most strategy resistant methods.)

Granted, though I think most Condorcet methods are rigorous. Schulze (by 
the beatpath definition) would give an objective to be maximized by 
reasoning that if there's a circular tie, the candidate that indirectly 
beats the others is preferrable. At the election methods level, 
"programs" and "functions" become very similar, and one may be phrased 
in terms of the other, generally speaking; it would be hard to make a 
functional description of say, first preference Copeland, or "Condorcet 
else IRV".

>> Independence of clones make the method resistant to
>> nomination (dis)incentives. Or rather, robust independence
>> of clones (not just "remove clones, then run through
>> method"), does. This is useful because one of the major
>> problems with Plurality is that it has a severe nomination
>> disincentive; if your candidate is similar to some other
>> candidate, you'll both lose. It's the other way with
>> Borda.
>>
>> I don't quite see what you're saying. The Democrat
>> candidates have a clear group preference order, whereas the
>> Republican candidates are looped; so something like:
>>
>> 50: D1>D2>D3>R1>R2>R3
>> 16: R1>R2>R3>D1>D2>D3
>> 17: R2>R3>R1>D1>D2>D3
>> 17: R3>R1>R2>D1>D2>D3
>>
>> A cloneproof method would act as if D* and R* are one
>> candidate (more or less). It may pick R3 instead of R1
>> because 18 instead of 16 preferred that one, but it
>> shouldn't switch from R* to D*.
>>
>> For the example above, Ranked Pairs / MAM gives the social
>> ordering D1 = R1 > D2 = R2 > D3 = R3.
> 
> Yes that's what I thought except that maybe the
> Democrats were neutral with respect to the
> Republican candidates (D1>D2>D3>R1=R2=R3) or had
> similar circular opinions as the Republican voters.
> 
> To me the interesting question is which one is
> better, D1 or R1. D1 doesn't lose to anyone. R1
> would lose (with the modified votes) to R3 quite
> badly (i.e. the voters would like to change R1 to
> R3 after R1 has been elected).
> 
> Should we then not elect the "most satisfying" D1.
> Or should we strictly stick to the ideal that if
> Republicans had not nominated R3 (that caused the
> problems to R1) then R1 would have won (if the
> votes had otherwise stayed the same).
> 
> Note that this violation of clone independence
> may not be a big enough threat to the parties to
> discourage nomination of more than one candidate.
> I guess it would be more typical that nomination
> of more than one candidate increases the
> probability of that party to win the election.
> (I also note that nomination of two candidates
> looks still very safe from this example point
> of view :-).)

Even if it had been D1 = R3 > D2 = R2 > D3 = R1, it would still have 
been cloneproof. I think I see what you mean, though; in a way, it's 
similar to the argument in favor of D'Hondt (as a divisor method among 
others) that parties can only gain by joining - there should be a 
disincentive to fragmenting.

Obviously, my example is a two-party situation, so yes, there a primary 
plus plurality would probably work as well, but it's a contrived example.

>> Would there be a situation where "first from a social
>> ordering" and "best single winner" would be
>> different in a single-winner election? If so, what is that
>> situation? (I assume there's no tie for first place.)
> 
> No. For one need, to elect a single winner,
> picking that single winner from the top of the
> social ordering should make no difference. I
> expect the society to determine the criteria
> well, and that should point out one of the
> candidate (or a tie). The tail of the social
> ordering is irrelevant (i.e. one could use
> different conflicting social orderings to
> point out the same single winner).

Which means that one may use Kemeny, which outputs a social ordering and 
minimizes a measure on potential orderings, to pick a winner (or more 
generally, any such method). If the tail of the social ordering doesn't 
matter, one can simply remove it afterwards (although I suppose that 
could lead to people asking why the metric should be on a social 
ordering scale in the first place).

>> Even with a method that permits truncation, parties may
>> tell voters how to vote. This happened in New York when they
>> used STV, and also in Ireland. Of course, there's a risk
>> that one'll overextend the vote management and thus lose
>> seats instead of gain them. Something similar could happen
>> with Condorcet "game of chicken" dynamics
>> regarding burial, if a sufficiently large group starts
>> burying. We don't have any data on the likelihood of
>> single-winner "vote management" (party-directed
>> strategy), though, simply because preferential single-winner
>> methods haven't been used long enough.
> 
> I see Condorcet methods as excellent methods if
> the level of strategic voting stays at random
> noise level. If majority of the voters start
> voting strategically, either in their own style
> or (worse) based on centrally coordinated
> strategies then I'd be willing to consider
> moving to use some other methods with which
> this particular society would work better
> (maybe down to Plurality and wait for things
> to settle). It is however quite probable that
> in many societies Condorcet methods would work
> fine (including Minmax).

I would rather have a Condorcet method on the strategy side of the 
Pareto front than plain old Plurality; or if the society's so interested 
in strategizing, use DSV Approval and set the human "grandmasters" 
against computers. That might be too complex, however, but would be a 
fair version of what might happen in any case if the base method allowed 
optimization/strategy: various parties would start using computers to 
find the ideal strategic vote.

>> Well, yes, but would the people? Of those that agree that
>> nonmonotonicity is a problem, would most also consider
>> reversal symmetry of no great importance? In the worst case,
>> people wouldn't understand Arrow at all, and the various
>> groups could end up using that to fling criterion failures
>> at each other.
> 
> We have seen that it is easy to generate all
> kind of bad examples, violations of nice
> looking criteria, biased terminology, and to
> ignore some of the weak spot's of one's own
> favourite method, and to emphasize different
> points in the right way. Election methods are
> complex enough and the example cases
> interesting enough to do this. For this
> reason I mentioned the unified front of
> respected experts. Maybe solutions like
> Wikipedia would work too, but also there
> I see lots of black and white for and
> against opinions. Maybe we are also lacking
> a scientific method based community of
> practical implementation related election
> method research with a popularization arm.

That's a good idea, and I think it would be useful if we were to move to 
an advocate stage. Create or find a group that's sufficiently scientific 
to understand the question and the methods, yet sufficiently independent 
to say "this seems best to me" outside of the context of EM messages. 
The other aspect of the method would be simplicity and the relative 
importance of criteria (how easy it would be to popularize, and what 
obstacles it may face from opponents), and that aspect would be more 
readily answered by potential voters (ordinary people), as those are 
after all who would be using whatever method one would focus on advocating.

>>> I'd appreceate e.g. a web site that would aim at
>>> neutral description of all the relevant methods
>>> (plausible candidates for election reforms), with
>>> estimates on how they would perform in real life.
>> How would we get those estimates? By testing the methods?
> 
> Since there can be many kind of tests with many
> kind of simplification and bias I'd trust also
> here a team of trusted experts or a scientific
> community with strong emphasis on seeking best
> results with respect to practical applicability
> of the results in real life.
> 
> Tests are often just very basic artifical models
> of real life situations. Therefore they need to
> be interpreted. And here we may need to trust
> the expert group or community to focus on the
> relevant aspects.

Yes, though simulations can be contentious. Consider, for instance, 
Bayesian regret.

> I btw trust also on simple example cases. They
> are useful in demonstrating how probable the
> benefits and vulnerablities are in real life.

Yee diagrams are good here, I think. The situations they model are ones 
that could practically happen; it's a lower bound of sorts - if a method 
shows odd results there, it would be suspect, but the converse may not 
be true.