On 01/30/2012 10:09 PM, MIKE OSSIPOFF wrote:
Does anyone here know the strategy of MJ? Does anyone here know what
valid strategic claims can be made for it? How would one maximize one’s
utility in an election with acceptable and completely unacceptable
candidates who could win? How about in an election without completely
unacceptable candidates who could win?
And no, I don't mean refer to a website. The question is do YOU, as an
MJ advocate, know what MJ's strategy is?
A maximally strategic MJ ballot (assuming certainty of all other
ballots) would be an Approval ballot with a strategic Approval
threshold, something like "approve of everybody you prefer to the
frontrunner you like most, then approve of him if he's got lower support
than the other frontrunner".
In other words, Range strategy.
The thing about MJ is that it's based on a robust estimator - the median
- and therefore, unlike Range, it's much less likely that your maximal
ballot will have a different effect than if you just voted honestly. So
if your default is to vote honestly (because you feel you should keep
some standard of fairness, for instance) - or the great majoriy prefers
to vote honestly - then you'll be much less tempted to vote strategically.
MJ doesn't actually punish strategists, however. It just ignores
strategy if not too many people are doing it. Warren used that fact to
claim that if you're rational, you should strategize in MJ too because
you lose nothing. In the worst case, his reasoning goes, you don't hurt
your candidate/s; in the best, you make him win.
That's why I say "if your default is to vote honestly", and I think
people would default to vote honestly if the temptation for strategy
wasn't too large. I have no proof of that, of course.
You could also use a feedback argument. Range strategy is really
obvious, so everybody knows how to do it, so a lot of people does it,
and the equilibrium then consists of a great deal of strategy. MJ, on
the other hand, robustly handles the case with a small minority of
strategists, so the strategists don't see their reward, so they revert
to honesty, making it harder to strategize for some other minority.
Again, that's a heuristic argument and I have no proof, but it seems
sensible.
But of course MJ differs from RV in the following way: In RV, if you
rate x higher than y, you’re reliably, unquestionably, helping x against
y. In MJ, of course that isn’t so. In fact, if you like x and y highly,
and at all similarly, and rate sincerely, then you’re unlikely to help
one against the other, at all.
Another difference is that, in MJ, even if you correctly guess that
you’re raising a candidate’s median, you can’t know by how much.
Suppose x is your favorite. y is almost as good. Say the rating range is
0-100. You sincerely give 100 to x, and 90 to y.
Say I prefer y to x, and, as do you, I consider their merit about the
same. If I rated sincerely, I’d give y 100 and x 90.
But, unlike you, I don’t vote sincerely. Because x is a rival to y, and
maybe also because I expect you to rate sincerely, I take advantage of
your sincerity by giving y 100, and giving x zero.
Same thing goes for Range.
At least in RV, you’d have reliably somewhat helped x against y.
Yes. That's what you pay to get MJ's strategy resistance. As MJ can't
divine whether your vote is honest or not, it must be similarly
insensitive to outliers whether they are honest (you really think y is
the second coming and x is worse than Stalin) or strategic. If enough
people strategize, then the filtering fails. If not, it works.
Another thing: Just as one example, try MJ on the Approval bad-example.
What you thereby find out is that, to be usable, MJ needs bylaws and
patches, such as to make it too wordy and elaborate (and arbitrary?) to
be publicly proposable.
If you're referring to candidates tending to have equal medians, the MJ
tiebreaker is simple. While two candidates have the same median, remove
median-rating votes from both candidates until one of the medians change.
----
Election-Methods mailing list - see http://electorama.com/em for list info
