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.
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.
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.
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.
The "ignorance problem" is addressed with runoffs when they are needed.
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."
What Kristofer has referred to is called the Later-no-Harm criterion.
Any system that efficiently arranges for social-utility maximizing
process *must* violate Later-no-Harm. I.e, the expression of a lower
preference *must* "harm the chance of the favorite winning." The key
word here is "efficient." There can be an LnH-compliant system which
exhaustively determines that candidates cannot win, and those are
then eliminated, but it's extraordinarily inefficient, requiring many
ballots. When it is done in a single ballot, it *must*, then,
eliminate, on occasion, the ideal winner.
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