Juho Laatu wrote:
--- On Mon, 1/12/08, Kristofer Munsterhjelm <[EMAIL PROTECTED]> 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?
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