[EM] Why I Prefer IRV to Condorcet

[Juho Laatu]

--- On Mon, 1/12/08, Kristofer Munsterhjelm <km-elmet at broadpark.no> wrote:

> > 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.
> 
> Then you should advocate Minmax for being Minmax, not for
> being Condorcet compliant. If you do the latter, then people
> may argue that the system is inconsistent because it
> doesn't follow up the implication of Condorcet
> (Condorcet loser, etc). But to my knowledge, you want to do
> the former, so I won't comment on this.

I don't have any strong promotional interests.
I like clarity and clear understanding. In this
case there is no need to refer to Condorcet
compatibility since Minmax(margins) can be
defined well (maybe better) without it.

Also the fact that the Condorcet winner vs.
Condorcet loser question is tricky may be a
reason to describe the method as Minmax. But
in general I do not fancy the idea of using
verbal tricks to make something look better
or worse than it is.

I'm thus ok with any definition. Minmax as
Minmax sounds good.

On the other hand minmax is a mathematical
term and adding "margins" there makes it
even more complex. For this reason also e.g.
"least additional votes", "least interest to
change" or "best pairwise result" based
names or short abbreviations could be ok
(for use outside the EM expert community).

> > 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.
> 
> I would have two reasons as well, but none of those you
> mentioned. It's possible to be cloneproof without being
> Smith and vice versa..
> 
> 1. Logical endpoint of mutual majority. A mutual majority
> set is one that a majority prefers to all else. Now consider
> a mutual dominant nth set. A mutual dominant nth set is a
> set that 1/n of all voters prefer to all the others, and
> where one of the candidates within wins, pairwise. Smith is
> just mutual dominant set with n->inf.
> 
> 2. Condorcet for sets. Smith is Condorcet for sets. If a
> set can beat all those outside the set pairwise, it should
> win. If the set is of size one, well, that's just
> Condorcet. The only reason why it should hold for size one,
> but not, say, size two, is if some other heuristic (like the
> Minmax metric/utility heuristic) is more important. If it
> is, see my first paragraph; but if we want this method
> primarily because it's Condorcet, or because the
> Condorcet idea itself is a good one, then we should be
> consistent and take that Condorcet as far as possible.

The mutual majority criterion is related to clones.
But it can also be seen as a criterion that refers
to the majority rule and life after the election.
I mean that some majority group may say after the
election "we want these candidates to win" and it
is difficult to explain that they will not get what
they want since they had conflicting opinions within
that candidate set on which one of them should win.

"Condorcet for sets" sounds a bit "aesthetics based"
to me since I don't know what practical real life
situation (other than aesthetic observations on the
graph that describes the pairwise preferences) could
be used to justify this criterion. If that set was
one candidate (or a nominated party/grouping) then
the basic Condorcet rule would apply, but if the
Smith set is just a random set of candidates and
there is no single majority group of voters behind
this group opinion then it is harder to find the
rationale. (The set members may not be clones and
there may not be a single set of voters that think
that this set is better than others.)

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)?

> In what situations would the single winner and the social
> ordering differ? It does, for proportional completion
> (because that's proportional and thus PR-esque thinking
> appllies), but to majority methods... I can't quite see
> when that would be the case.

No need to be different. I was just thinking
that they may be used for different purposes
and therefore may be different.

> > 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.)
> 
> It's easy to make a voting method
> "cloneproof" in this manner. Just have a prefix
> that collapses clones down to single candidates, then if any
> of those pseudocandidates win, pick the one that's
> closest to winning were the clone candidates not collapsed.
> But that would be a very fragile cloneproof condition
> indeed.
> 
> Consider something like this:
> 
> 1000: A>B>C>D>E
> 1021: D>A>B>C>E
>  874: E>D>A>B>C
>  760: C>B>A>D>E
> 
> (Schulze gives D > A > B > C > E)
> 
> {A,B,C} are clones, and the prefix method would replace
> them with a candidate of its own. But now consider this:
> 
> 1000: A>B>C>D>E
> 1021: D>A>B>C>E
>  874: E>D>A>B>C
>  760: C>B>A>D>E
>    1: C>D>B>E>A
> 
> (Schulze still gives D > A > B > C > E)
> 
> Now they're not strict clones anymore. A good method
> should recover gracefully from this condition, since in real
> world elections, it's very unlikely that all voters
> would vote the clones exactly in the way to make them
> obvious as clones. The prefix wouldn't do that.

Yes, methods should not identify clones strictly
as in the clone definition. The transitions should
typically be smooth.

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.

> > 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.

> >> 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 :-).
> 
> 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.

There are many viewpoints in the comparison.
1) True targets (which candidate should be
elected, PR, regional proportionality)
2) Strategic opportunities (or the lack or
insignificance of them, or need to fix some
current problems)
3) Political realities (required steps from
the current system, risk of electing outside
of the current major players)
4) Popular claims, positive and negative
descriptions and example cases, tuned
terminology, strong persons with strong
opinions

> This could happen even with the
> kind of criteria we think are not very important
> (Consistency, Participation, or LNH* for a method that fails
> both LNHs), but it would carry greater weight for those
> criteria that are meaningful ("they say IRV spoils
> candidates, but with Nanson, it's not even
> cloneproof!" or whatever).
> 
> As for experts, again we hit the problem of estimating how
> much strategy would happen. Ideally, we'd either have
> that data or we'd have some way of saying "all we
> mean is that Condorcet is good: if you want something good
> but possibly complex, choose this, otherwise..", and
> unite under Condorcet. Perhaps some sort of "here's
> the criteria the different methods pass, pick what you think
> would be best", but I think knowing real world strategy
> so we could find a single Condorcet method would be better.

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.

Juho