[EM] Why I Prefer IRV to Condorcet

[Kristofer Munsterhjelm]

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

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.

>> 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.

I'm considering the majority rule interpretation; otherwise, I could 
just have gone straight for independence of clones. I defined a mutual 
dominant set above, and for small values of n, one could reasonably 
expect parties (or those who support them) to wonder, if the method is 
Condorcet (thus candidates that pairwise beat others are good 
candidates), and supports majority rule (thus mutual majority etc), why 
it doesn't elect from the mutual dominant nth set. If you have Smith, 
you can ensure that it does, no matter how large n is.

> "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.)

I suppose this leads back to clone independence, so I won't address it 
here, except to say that majority for a set makes sense (Mutual 
Majority; at least it does to me), and so should Condorcet for a set.

> 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.

>> 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.

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.)

>> 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.

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.

>>> 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.

>>> 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.

>> 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.

How would we get those estimates? By testing the methods?