On 12/14/2012 08:26 AM, ⸘Ŭalabio‽ wrote:
2012-12-13T06:53:10, Kristofer Munsterhjelm:
- If the voters know that +99 and -99 will be discarded, that
effectively turns +99 and -99 into 0. Thus they'd not use those values,
instead knowing their "real maxima" to be +98 and -98.
Yes, but they have to give at least 1 candidate has to get a
negative
-99 and another has to get a positive +99. The could hive those score to
other candidates and give negative -98 to their most hated candidate and
positive +98 to their favorite, but when removing the top and bottom 3rd
in the next step will likely remove both the negative -98s and the
positive +98s too. It is hard to find a way to strategically vote in
this system.
In one sense, it's true, but in another, the problem remains. To show
the problem, let's call +99 "Q" and -99 "R" just to show that the
argument doesn't depend on the values of the ratings you'll be throwing
away.
Then, to a game-theoretically rational voter, Q and R are effectively
"no opinions", because they're not going to be included in the count. So
his strategy should be to give Q and R to parties or candidates of which
he has no opinion (and thus don't want to say anything about). Whether Q
is called "+99" or "+50" doesn't matter.
The requirement that the voter spend at least one Q and R makes strategy
a little harder. However, it's not all that much harder. If the voter
knows there are two no-hopes that have no chance of winning, he could
spend his Q and R on them. More precisely, if there are candidates that
are either sure to win or lose, the voter can allocate Q and R to them.
If enough voters feel this way, some of them may nominate a "throwaway
candidate" for that purpose.
If I were to make a method with the logic of throwing out extreme
ratings, I would use a truncated mean or something similar (e.g.
Winsorising) that is general instead of specific. That is, if you have a
10% truncated mean, it's going to throw away the upper and lower 5% no
matter whether those ratings are +99 and -99 or +98 and -98. In
contrast, your method may give a different result if every voter halved
the range he was going to vote over (if he could), which seems pretty
strange.
- For any given society, there's probably some optimum such level
if you want to use utilitarian voting.
Perhaps. That is a great open question.
If utilitarian voting is Range-like, then you effectively have a
trade-off between resistance to strategy (higher breakdown point is
better) and responsiveness to honest voter input (higher statistical
efficiency is better).
I think the trade-off between strategy and performance is also present
in ranked voting methods. Say you have an election (ballot set) called
E_a. In E_a, the best choice if all the ballots were honest is to choose
winner A. However, say another ballot set E_b can be transformed into
E_a by people that prefer A to B executing some strategy (i.e. lying on
their ballots), and that similarly, under honesty, the best winner for
E_b is B.
Then if your creating a method, and your method values honesty, it
should pick A when given E_a. But if your method is supposed to resist
the A-voters' strategy in the case of E_b, it should pick B when given
E_a. You can either have it elect A (in which case you get better honest
performance) or B (in which case you get better strategy resistance).
The method itself can't read the voters' minds so it can't know if E_a
is the real deal or a strategized E_b, so it has to *assume* one way or
the other.
- If everybody strategizes no matter what out of the reasoning that
"voting strategically can't harm me so I'll do it even if it probably
won't help me either, because there's a probability epsilon> 0 that
everybody else will think so too, and then I better get mine", then it
really doesn't matter what you'll pick - it'll all go to Approval anyway.
Degrading to Approval Voting is not bad. Approval voting still beats
Plurality.
Beating Plurality is a pretty low bar :-)
- If more than a majority strategizes, you have no chance of
respecting the honest votes, since it's impossible to determine which
votes *are* honest.
No system is perfect. We need to try to find a system as resistant
to strategy as possible. That is all we can do. This system definitely
resists strategic burial and strategic exaggeration.
Oh, I wasn't saying your method doesn't resist strategy. I was just
outlining how far it's possible to go, in general.
- If there are lots of strategizer-hedgers (who'll strategize even
when it's pretty certain it won't help), but not a majority, MJ deals
better with that than does Range.
Perhaps. In mine humble opinion, Majority-Judgement needs more testing.
You might be interested in
http://hal.archives-ouvertes.fr/docs/00/24/30/76/PDF/2007-12-18-1691.pdf
, "Election by Majority Judgement: Experimental Evidence", which is
about just that. It details MJ exit polls in France, as well as what the
data from these exit polls suggest.
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