[EM] Why I Prefer IRV to Condorcet

[Juho Laatu]

--- 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.

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).

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.

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.

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.)


> > One should also ask if the clone criterion is ideal.
> > For strategy reasons sufficient independence of
> > clones may be necessary to make it safe for
> > parties/wings to nominate more than one candidate
> > (or to nominate only one).
> > 
> > How about the following situation. Both Democrats
> > and Republicans have three clone candidates. All
> > votes are sincere. Both parties have 50% support.
> > The Democrat candidates have a clear group
> > preference order. The Republican candidates are
> > badly looped. Is the fact that electing a
> > Republican candidate would leave us in a
> > situation where majority of the voters are
> > not happy but would like to replace this
> > candidate with another candidate a sufficient
> > reason to elect the best Democrat candidate
> > instead. I.e. should we be fully independent of
> > clones or should we elect the candidate that
> > seems to be the best compromise candidate /
> > most agreeable (=least opposition in any
> > pairwise comparison)?
> 
> 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 :-).)


> 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).


> > There are many ways to identify the clones.
> > Beatpaths is one approach. Another solution
> > would be e.g. to allow the candidates to
> > declare themselves as clones.
> 
> This could work for a method with a vote-splitting
> weakness. In that respect, I suppose it would be similar to
> fusion parties, or my "artificial Condorcet party"
> idea. However, no candidate would want to declare himself as
> clone of somebody else in the context of a system with a
> teaming-type weakness. Also, I don't quite see the
> reason to do this (compensate for clones) explicitly if one
> can have a method that does it implicitly.

Just one option. Other approaches may not be
perfect / ideal for he need either.


> >>> In Condorcet vote management could be the
> >>> most probable path leading to "too high
> >>> levels" of strategic voting. In large
> public
> >>> elections with independent voters the risks
> >>> are at rather low level.
> >> Do you mean the risks from vote management, or
> >> non-vote-management strategy?
> > 
> > I was thinking something like the Australian
> > situation where voters are used to vote as told
> > by the parties in the how-to-vote cards. This
> > makes it possible to apply strategies that would
> > not be possible with voters that make independent
> > (heterogeneous) decisions.
> 
> Yes. What does the how-to-vote situation in Australia show
> us? In my opinion, it shows that the election method should
> not demand full ranking, and that in any event, how-to-vote
> cards should not be made part of the official process.
> I'm not sure if they are in Australia, but
> above-the-line voting is pretty close.
> 
> 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).

 
> >>> A unified front of respected experts could do
> >>> a lot. Unfortunately all the experts seem to
> >>> have their own favourite methods and
> >>> corresponding campaigns :-).
> >> That was a reference to Minmax. If you throw
> >> nonmonotonicity at IRV, they might throw reversal
> symmetry
> >> failure at you in return.
> > 
> > I wouldn't mind that since I don't see
> reversal
> > symmetry as a requirement for group opinions on
> > single winners. I sort of expect the society to
> > be mature enough to handle also the tricky
> > questions in some rational way.
> 
> 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.


> > 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.

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

Juho