[EM] Truncation (was re: Defeat Strength)

[Forest Simmons]

On Wed, Sep 14, 2022, 2:19 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> 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.


I strongly doubt that quantitative considerations of utility help the
average voter decide between A>B,  A= B, and B>A.

It might be relevant in a Borda election with sophisticated voters, but not
in a Benham election with English "ploughboys voting" as Dodgson put it.

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.


It looks to me like you are stuck in the Borda mode with sophisticated
voters.

In an ordinary  Benham election, if the voter feels ever so slightly that
her A>B preference is stronger than her B>C preference, it would be
completely appropriate to express that as A>>B>C.  Unlike in the Borda
context, the double chevron does not imply that >> is approximately twice
as strong as a single chevron preference.

It's precisely analogous to a voter deciding to vote X>Y instead of X=Y
even though the preference is very weak. The voter is not dishonest in
expressing a strict preference even though the utility difference between X
and Y might be a tenth order infinitesimal.

But how much?
>

The whole point of ranked rankings is the preference strength is
qualitative rather than quantitative, just as ordinary rankings are
qualitative rather tha quantitative.

Otherwise, instead of ranked-rankings, we would be talking rated-rankings,
really a more appropriate name for the Borda analog I regrettably
introduced under the wrong name.

I did warn everybody that it was only one interpretation of the multiple
chevron notation ... but I should have known nobody would pay attention
that caveat.

My original use of the notation was with "dyadic approval" twenty years
ago. In that context there were two main applications .... the primary one
was for approval elimination. The secondary one was a shorthand for binary
ratings ... a form of decloned Borda, really.

>
>  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
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