[EM] An hypothetical voting system based on Score-Voting and Majority-Judgement which I do not advocate.

[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.

- 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.