[EM] Why I Prefer IRV to Condorcet

[Juho Laatu]

--- On Sun, 14/12/08, Kristofer Munsterhjelm <km-elmet at broadpark.no> wrote:

> 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).

Yes. We may complain when the favourite
of the strategists is elected with some
set of votes. But we should also always
ask the question who should have been
elected if we would have a similar set
of sincere votes (or if some other group
of strategists changed the votes in the
reverse direction).

> 
> > 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 Condorcet methods have at least
passed one of my tests. I have several
times asked the election method experts
to give a simple set of strategic rules
that voters could apply in Condorcet
elections for their benefit. But I have
not seen any. The next task would be to
point out real life like election
examples where strategies are easy and
riskless enough so that they could be
publicly recommended to voters (in typical
large public elections). Also this has
been quite difficult to achieve. One
could also try to find out strategic
opportunities in coming real life
Condorcet elections and try to find
good strategic advices for voters in
them. I haven't seen this either.
All this does not prove that Condorcet
would not fall in some scenarios, but
at least this shows some direction and
something about the typical behaviour.
(Also methods that are currently widely
used do have vulnerabilities.)

> 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.

Real life testing is probably the best
thing to do.

> 
> > 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.

If there is a target of avoiding
fragmentation that should be clearly
stated. Otherwise that property should
be counted as a flaw.

Same with Condorcet methods. One
should make it clear if the target is
e.g. not to hinder nomination of
multiple candidates per party.

(And one should directly or indirectly
also say if is ok to count losses to
other candidates as "negative points"
also when all those candidates are
(according to some measure) clones of
the candidate in question.)

> 
> 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).

Yes, although it might look strange if
changes in the social ordering somewhere
down below would in some cases change
also the most preferred candidate.

> 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.

(Note btw that finding the ideal
strategic votes for all the voters
is typically easier than also
implementing that strategy in real
life elections.)

> 
> >> 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.

One basic requirement in a democracy
is also that the (decision making)
citizens do understand how the system
works. They are not cattle but the
ultimate decision makers that need to
understand both the content and the
working methods at some suitable
level. Clear modelling and clear
descriptions are this essential to
make a democracy work better.

This is of course quite important
especially in complex areas like
voting methods and the related
mechanisms and behaviour of democracy
in general. Good modelling and
presentation needed to make any
progress.

> 
> >>> 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.

Yes, they all need good interpretation.
I also often think that the society is
in any case a more complex animal than
what the simplifying theories and
models describe. That means that in
order to explain one may need a bit
wider understanding of the environment
than just mechanical understanding of
the used tests and simulations, simplified
criteria, simplified requirements etc.
Definitions, simulations and models can
also be built to present only one
viewpoint to the topic in question.

> 
> > 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.

Yes, nice pictures that offer good
information on what the utility
function of each method looks like.
Also they (and their limitations)
need to be explained well.

Juho