On 12/10/2012 05:12 AM, ⸘Ŭalabio‽ wrote:
¡Hello!
¿How fare you?
While explaining advanced voting systems to Bronies and PegaSisters,
I had an idea about combining the expressiveness of Score-Voting and
he resistance to tactical voting of Majority-Judgement. This is the
line of thought leading to the idea:
Majority-Judgement rests tactical voting by filtering out extreme
values which may be do to tactical voting. This is the way the
voting system would work:
0. Voters give their favorite candidate a positive +99 and their most
hated candidate a negative -99.
1. The voters then score other candidates relative to the 2 extremes.
2. After counting the votes, the counters throw out all of the
negative -99s and the positive +99s.
3. The counters remove FROM THE REMAINING BALLOTS the top 3rd
plus + 1 ballot and the bottome 3rd plus + 1 ballot.
4. The counters then average the scores.
5. Highest average wins.
I've been really busy of late, but here are some short comments:
- 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.
- Throwing out the upper and bottom third (plus one) can be considered
somewhere on the scale between median (throws out everything but the
middle) and mean (throws out nothing). By going from the median to the
mean, you give strategic resistance (the "safety level" where nothing
happens if you strategize) in order to get more utilitarian behavior
under honesty.
- For any given society, there's probably some optimum such level if you
want to use utilitarian voting.
- 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.
- 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.
- 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.
- In general, there's an equivalence to robust statistics. The median
works even when a majority minus one of the samples are suspect. The
mean, however, can get arbitrary off target by a single outlier. AFAIK,
though, the relation isn't exact: the breakdown point only gives how
many values can be wrong in one direction with the statistic still
giving the right result, whereas strategy can exaggerate in both
directions. (Tell me if I'm wrong here.)
- Even if you widen the range considered just a little from the median,
you get a method that fails the majority by grade criterion. The
invariance under nonlinear monotone transformations no longer applies
either. As such, the method should be considered utility-based, like
Range, not grade-based like MJ.
- Other grade-based methods include: greatest best grade and greatest
worst grade. These are probably not as robust.
- Various types of Range DSV have been made to try to preserve the
utilitarian nature of Range while making it more robust to strategy.
Some of these fail criteria like IIA even when the voters evaluate
candidates rather than comparing them; but that is not the case for all
Range DSV variants that have been proposed.
I think that's right. I'm writing this quickly, so it might not be.
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