[EM] Truncation (was re: Defeat Strength)

[Kristofer Munsterhjelm]

On 9/14/22 09:36, Juho Laatu wrote:
> In addition to that, I still have some interest in the ranked 
> rankings style votes (A>>B>C) where one preference step is considered
> more important than another step (forming a tree of preferences or
> something like that). I have not done my homework on this (been lazy
> for the last decade). Do you know if that approach would likely
> suffer from some (strategic voting or vote counting complexity
> related) problems that would make it unusable?

I think there would be a problem defining just what it means in the 
honest case. Consider ranked ballots from a utility perspective: A>B 
means that my utility for A is greater than my utility for B. Then 
consider something like A>>B>C. Presumably this means that I like A a 
lot more than B, and then I only like B a bit better than C. But how much?

 From one perspective, you could use normalized ratings and say A>>B if 
the difference between A's rating and B's rating is k or more. But then 
you could just use ratings directly. To me it seems that hierarchical 
preferences would just make for a very hard ballot to fill out.

One benefit of ordinary preferences is that they're unaffected by affine 
scaling: if I think B is the next Stalin and I'm OK with A, my 
preference is A>B, and if you think B is OK and A is great, your 
preference is also A. The problem of (non-normalized) ratings is that I 
don't know what one point difference is: is it the difference between 
excellent and good, or between good and awful? Hierarchical rankings 
lose that benefit because you have to know just how much of a change 
merits an additional >.

As an inbetween between rankings and full (necessarily normalized) 
ratings, I would probably suggest MJ's grade scale instead. If there is 
a common agreement on what an additional > means, then I think it's more 
intuitive for the voter to grade A Excellent, B Poor, and C as Reject, 
than it is to vote A>>B>C.


On a side note, it would be interesting to devise a normalized ratings 
method that maximizes VSE on a spatial model. The normalization 
criterion could be something like "if the scale is unbounded and we 
apply a monotone affine transformation to a ballot, then the outcome 
shouldn't change".

-km