[EM] Truncation (was re: Defeat Strength)

[Kristofer Munsterhjelm]

On 9/15/22 05:11, Forest Simmons wrote:
> 
> 
> On Wed, Sep 14, 2022, 2:19 AM Kristofer Munsterhjelm 
> <km_elmet at t-online.de <mailto: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.

I might have overcomplicated things. I was simply trying to formalize 
that whether a honest voter votes A>B, A=B, or B>A depends only on his 
preferences (which are unambiguous) and neither on the method or the 
strength of that preference, apart possibly from A=B, where concerns of 
precision come into account.

My point is that I'm not sure how you could make a similar 
method-agnostic unambiguous definition of what it means for an honest 
voter to vote A>>B instead of A>B.

I guess I'd very much like honest voters to just be able to vote their 
preferences without having to concern themselves with what method is 
doing the counting or which honest vote is the right one.

> 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.

That suggests to me that, in a utilitarian model, you'd vote A>>B if you 
voted C>D and (utility of A - utility of B) > (utility of C - utility of 
D). And similarly that you'd vote E>>>F if there's an A>>B so that 
(utility of E - utilify of F) > (utility of A - utility of B).

Which at least gives an idea of how such notation could be independently 
defined :-)

It feels to me, though, like it would be easier to just ask for ratings, 
making clear that strengths of preference aren't directly taken into 
account (because it's not really a cardinal election), and then have the 
method calculate which gaps are the largest.[1]

That is, in terms of user experience, it feels like asking for something 
like (A: 22, B: 11, C: 8, D: 20, E: 31, F: 0) is much easier than asking for

E>>>>A>D>>>>B>>C>>>F

where

 >>>> = rating difference 9
 >>> = rating difference 8
 >> = rating difference 3
 > = rating difference 2

At least it was for me :-)

-km

[1] This poses no problems to von Neumann-Morgenstern because rankings 
of differences are unchanged over arbitrary positive affine 
transformations. Which is another way to say, like you did, that they're 
qualitative.