[EM] Quick and Clean Burial Resistant Smith, compromise

[Kevin Venzke]

Hi Kristofer,


Le lundi 17 janvier 2022, 06:00:34 UTC−6, Kristofer Munsterhjelm <km_elmet at t-online.de> a écrit : 
> I'm surprised that STAR is such a poor performer, though! (How about
> IRNR_p? This is IRV-style elimination of the loser, except after each
> step, the original rated ballot has the eliminated candidates removed
> and then the ballot is rescaled to have unit p-norm. Try p=1,2,infinity.)
> 
> I guess the hunt's still on for a cardinal method that really resists
> strategy. There's Hay voting, which is a strategyproof method (under VNM
> utilities), but it has predictably awful honest performance, just like
> Random Ballot has in the ranked domain.

I was looking into IRNR_1 recently because it occurred to me I had no idea where
it plots in my method space. (I should say, that I have to infer ratings from
the rankings in order to do this at all.)

So I implemented it and found it not so similar to anything. It's kind of
strange when I really think about it. If the rating scale is 0 to some positive
number, to normalize the ratings means that you dilute your voting power more
by casting a bunch of high ratings than by a bunch of low ones. That reminds me
of cumulative voting. I can't think of why it ought to behave that way.

Brian Olson has a pdf suggesting he envisions the use of positive and negative
ratings. I can't quite picture the effect of that, except that it seems a lot
more likely to produce sums of zero so that you don't know how to normalize it.

Furthermore, unless I've totally misunderstood, given how the normalization
works, IRNR doesn't guarantee to elect the pairwise winner between the last two
candidates.

I instead tried Instant Runoff "Rescaled" Ratings or "IRRR" where all you do is
adjust the ratings among remaining candidates so that they use the entire rating
scale. This plots in more familiar territory, about midway between the WV
methods and C//IRV. Though I doubt it's a method you're looking for.

As far as IRNR's properties, what I found was:
Low compromise incentive, though I think this may be illusory in some way. (For
example, a method that ignores all input will have zero compromise incentive.)
Lower burial incentive than C//IRV. So good.
Monotonicity about the same as IRV, but add some mono-add-top failures too.
Very high truncation incentive, can be even worse than Bucklin.
Poor Condorcet efficiency, sometimes worse than Bucklin.

Kevin