On 06/16/2013 06:18 PM, Abd ul-Rahman Lomax wrote:
At 02:02 AM 6/16/2013, Kristofer Munsterhjelm wrote:
It would work, but the rating variant is better. In the context of
ranking, Bucklin fails Condorcet, for instance.
Straight Bucklin does fail Condorcet, of course, as do straight Range
and Approval. However, we can tell from the fact that Range fails
Condorcet that there is a problem with the Condorcet Criterion, one of
the simplest and most intuitively correct of the voting systems criteria.
Your first claim is right, of course. It is also right that I'd never
want to have Range used as a straight ranked system. Depending on how
you implement it, ranked Range becomes Borda, Plurality or
Antiplurality, neither of which are very good.
I don't think your second claim follows, though. Condorcet might be a
bad criterion to apply to a rated or grade-based method (because it
doesn't take preference strength into account), but that it is a bad
criterion in general doesn't necessarily apply. In the case of a ranked
method, like say the original Bucklin, you don't *have* preference strength.
The problem also applies to the Majority Criterion. Those criteria do
not consider preference strength. Practical, small-scale, choice systems
do, routinely. They do it through deliberative process and repeated
elections, vote-for-one, seeking a majority. And then, a process that
can even review a majority choice and reverse it, where preference
strength justifies it.
Thus a deterministic single-poll method that optimizes social utility,
and that collects information allowing that, *must* violate the criteria.
And that's a problem, because this is a fundamental principle of
democracy: no binding choice is made without the consent of a majority
of those voting on the issue. Some are aware of the "tyranny of the
majority," but solutions to *that* cannot be found in deciding *against*
the preference of the majority, *without their consent.* The result is
minority rule, not broader consensus.
And that's kind of the thing I'm talking about. Ranked ballot methods
don't have preference strength data. In that case, ruling in favor of
the majority is better than doing so in favor of the minority. Of
course, it would be better to not have to make that choice in the first
place, but my point is that if you consider Bucklin, the ranked method,
then it has to make a choice one way or another. And between the choice
of making assumptions that makes it fail Condorcet, and making
assumptions that makes it pass, the latter is preferrable. That is also
what ranked Bucklin does.
But my point is that while rated Bucklin (MAV) might be a good method, a
ranked quantization of it might be worse than other ranked systems that
exist: simply because in the rated version, the weirdness is less
relevant since it doesn't have to make assumptions the ranked version does.
So there is a solution: repeated election. Over the years of considering
this problem, I've concluded that with the use of advanced voting
systems, such as Range methods, and good ballot analysis in a first
round, with a runoff where a majority decision is not clear, such that a
Condorcet winner in a primary will *always* make it into a runoff, in
addition to one or more social utility maximizers, it is possible to
1. Find a majority choice, almost always, in two ballots, with the
exceptions being harmless.
2. Satisfy the Majority and Condorcet criteria.
3. Optimize social utility.
These have been considered opposing goals. That is because
1. Voting systems study has neglected repeated ballot.
2. Voter turnout has been neglected.
3. The electorate has been assumed, where runoffs have even been
considered, to be the same electorate with the same opinions. Neither is
real.
And that would be a system that gets around the problem by not having to
make an assumption. For instance, when MJ/MAV fails Condorcet, or when a
Condorcet method picks a Condorcet winner, and you're right about the
differences in voter turnout fixing things, then the runoff can
distinguish a weak CW from a strong CW -- or a candidate that fails
Condorcet for good reason from a candidate that is picked by MJ because
of artifacts in MJ/MAV itself.
It also has some bullet-voting incentive. Say that you support
candidate A. You're reasonably sure it will get quite a number of
second-place votes. Then even though you might prefer B to A, it's
strategically an advantage to rank A first, because then the method
will detect a majority for A sooner.
This is somehow assumed to be "bad." That incentive exists if there is
significant preference strength. Thus "bullet voting" is a measure of
preference strength, i.e., is useful in measuring social utility. There
is, however, another cause for bullet voting: voter ignorance (which is
natural and normal). A voter simply may not know enough about another
candidate to vote for the candidate. And this is probably the major
cause of bullet voting, historically, with Bucklin, combined with high
preference strength.
Or it could simply be partisan gaming of the system. With only ranks,
and only one round, there's no way to know.
(As I have said before with regard to LNHarm and LNHelp, at least for
ranked methods, I prefer a method that fails both to about an equal
degree, to one that passes one and fails the other.)
One of the points of the graded/rated variants is to encourage the
voters to think in absolute terms ("is this candidate good enough to
deserve an A") rather than relative terms ("is this candidate better
than that candidate"). If they do, then the method becomes more robust.
If somehow we could extract absolute utilities from the voters, sure.
However, real-world, people make choices based on relative utility, not
absolute utility. Imagining a voting system as becoming more "robust,"
if voters behave utterly unrealistically, depends on a rather strange
idea of "robust." We *are* machines, but we are programmed to optimize
among *choices*. Our very assessment mechanisms are relative to what is
"espected as realistic possibilities."
But doesn't B&L's experimental evidence show that the voters *can* think
in absolute terms? Not exactly in utility-normalized ones, but in terms
where the comparison points are set? For grades, the distance between A
and B might be greater than the distance between B and C, but for MJ,
that doesn't matter. I don't think it matters for other Bucklin variants
either, though I am less sure of that.
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