[EM] An hypothetical voting system based on Score-Voting and Majority-Judgement which I do not advocate.
⸘Ŭalabio‽
Walabio at MacOSX.Com
Thu Dec 13 23:26:44 PST 2012
2012-12-13T06:53:10, Kristofer Munsterhjelm:
> 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.
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.
> - 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.
¡Exactly!
> - 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 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.
> - 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.
> - 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.
> - 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.)
You are right. This system should be hard to game, hopefully. It is untested, so we do not know what will happen. Perhaps we gan ask Professor Warren Smith to check its Bayesian Regret and draw a few Yee-Diagrams for us. If any of these 3 things happen, we should reject it:
* High Bayesian Regret
* Prefers extremists
* Randomly chooses winners
Any of those are deal-breakeers.
> - 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.
Okay.
> - Other grade-based methods include: greatest best grade and greatest worst grade. These are probably not as robust.
It is not a grading system, so I do not worry about those.
> - 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.
We shall have to experiment to find out how this system does.
> I think that's right. I'm writing this quickly, so it might not be.
You seem right to me.
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