[EM] Majority Judgement

Jameson Quinn jameson.quinn at gmail.com
Wed Feb 1 09:15:06 PST 2012

On 2012 1 31 01:45, "Kristofer Munsterhjelm" <km_elmet at lavabit.com> wrote:
> 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".

Actually, if "maximally strategic" means "favorably changes the margin of
victory" (the minimum number of ballots that would haved to change to
change the utility of the outcome), then it only requires voting the two
distinct frontrunners on opposite sides of the winning median. If those
frontrunners are ideological opponents, chances are high that an honest
ballot accomplishes this. If the two frontrunners are ideological
near-clones from an opposing ideology, it is likely that their utility is
about the same, so that the next frontrunner whose utility is distinct is
ideologically opposed, and we're back to the previous case. So probably the
only time strategy is an issue is in the chicken dilemma case, where the
frontrunners are near-clones from a favored ideology. And in this case, the
unswerving strategy is not meta-strategic; an ideological group which tends
to be unswervingly strategic against its allies will tend to lose to its
opponents. So basically, in all common cases there is at least a reasonable
presumption that honesty is justifiable.

I should also talk a bit about zero-knowledge strategy. Even if you don't
know anything about the popularities of the particular candidates involved,
you still have robust statistical and historical reasons to believe that
the winning median will be something around the middle score or slightly
above. So even if you are relentlessly strategic, you can be almost sure
that you are using the correct zero-knowlege strategy without maximally
exaggerating. For instance, on the 6-level ballot that Balinsky and Laraki
suggest, you could just avoid the middle two ratings (and perhaps once we
have better statistics on historical elections, that might shrink to 1 or
even 0 ratings to avoid). This has important psychological effects; since
you still have expressive room to make a distinction between your favorite
and an acceptable compromise, there is less of an impulse to
unstrategically bullet vote than there would be under approval.

> 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.

Well said.

> 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.

I agree.

>> 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.
> ----
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