[EM] Why I Prefer IRV to Condorcet

[Juho Laatu]

--- On Thu, 27/11/08, Kristofer Munsterhjelm <km-elmet at broadpark.no> wrote:

> > 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).

I didn't quite get this. When evaluating
candidate X minmax just checks if voters
would be interested in changing X to some
other candidate (in one step), while
methods like Schulze and Ranked Pairs may
base their evaluation on chains of victories
leading to X.

> > 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.

There are different kind of criteria.
If one decides the winner based on one single
vote a method that would elect the least
preferred candidate would be bad. Things get
however more complex with group opinions that
may contain cycles. Then it is possible that
some candidate loses to every other candidate
but still is the most liked one in the sense
that there is only a very weak interest to
change that candidate to some other candidate.

> >> 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.

Yes, I assumed that in this case the society
had chosen minmax as a sincere utility
function that determines the best winner.

> 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).

I can see two kind of reasoning that people
may use to justify the use of Smith set as
a criterion that determines the best winner.

1) Clone based. Smith set is some sort of an
approximation of clone candidates. Smith set
is however wider (wider than the set of
candidates that are next to each others in
every ballot). (Note also that candidates
that are next to each others in every ballot
need not be clones in the sense that they
would be ideologically similar.)

2) Drawing technique based. When drawing a
graph that represents the results of the
election one typically draws the Smith set
candidates at the top of the paper, and all
the other candidates below that group. Since
people intuitively model also group opinions
as linear preference chains this drawing
technique may give them a false impression of
the group preferences. The problem is that
this drawing technique hides the defeats of
the Smith set members to each others.

> > 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.

My statement was not quite accurate. I should
have said only that the criteria for
determining the social ordering and the best
winner in some single-winner election may be
different.

> 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...

I think it would be good to agree on the
target first. For example the target of
making U.S. a multi-party democracy is quite
different from the target of removing the
problem of small party spoilers in the
presidential elections. And promotion of
one's favourite method at all cost is yet
another quite different target.

> > 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?

Here's an example of what I was thinking.

2: A>B>C>D
2: B>C>A>D
2: C>A>B>D
1: D>A>B>C
1: D>B>C>A
1: D>C>A>B

A, B and C are clones in the sense that they
are next to each others in every ballot. A, B
and C also form a Smith set.

3: A>B>D>C
3: B>C>D>A
3: C>A>D>B

With these ballots the resulting matrix (and
Smith set) is exactly the same. But A, B and
C are not next to each others in any of the
ballots.

> 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".

As demonstrated above clones (as typically
defined) can not be derived from the matrix
alone. Also ballots are needed.

Yes, one could replace sets of clones with
some virtual candidate. If that virtual
candidate wins then one can use some further
"completion method" to determine the winner
within that clone set.

I have also played with the idea of allowing
the candidates themselves to indicate which
of them should be treated as clones. That
would guarantee that all clones and only
clones are treated as clones.

(One could go also further and allow
hierarchies of clone groups.)

> > 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).

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.

> 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.

My theoretical approach to the problem of
having many different Condorcet (and other)
methods is that there may be many utility
functions that one may choose. In some cases
there might also be a need to strengthen the
methods and make them more strategy resistant
(at the cost of not always electing the best
winner according to the agreed utility
function).

My practical approach might be to pick a
representative set of Condorcet methods and
say that they are all good.

These election method evaluation questions
are tricky. It is very difficult to explain
all the relevant factors. And on the other
hand it is easy to develop various threat
scenarios that can be used against other
methods.

A unified front of respected experts could do
a lot. Unfortunately all the experts seem to
have their own favourite methods and
corresponding campaigns :-).

> > 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.

Yes, that is a good approach that introduces
new good methods to the voters. One could
market these services also to TV shows etc.
to get lots of publicity and experience in
large elections. That would demonstrate the
viability of these methods (and ability to
cast sincere and informative votes without
any strategic voting related needs and fears)
also for use in political elections.

Juho