[EM] Winners or representation?

[Kristofer Munsterhjelm]

On 03.04.2022 11:54, Richard Lung wrote:
> 
> It’s putting oneself at an unfair disadvantage to try to prove something
> that doesn’t exist. The term “winners” assumes some preordained election
> results, that one has to try to discover. The statistical assumption, as
> distinct from the determinist assumption, is that there are only best
> estimates of representation. Some candidates win beyond reasonable
> doubt. Other contests may leave the voters indifferent, with no
> candidates a clear winner. This is just a fact of life that defies
> mathematical certainty.

An estimator can itself be deterministic without making the process of
estimation deterministic. And properties can be proven about these
estimators (e.g. whether they're biased or not); it's not like these
properties don't exist.

So too with voting methods: you may from a statistical perspective
consider voting methods to be estimators of some parameter (this analogy
is particularly direct for Kemeny).[1] That the methods respond in
predictable ways given predictable data does not make them deterministic
when applied to random variables any more than it does the sample mean.

Perhaps we could replace the term "winner" or "winning set" with
"estimated best fit". But this would not affect whether voting method
criteria exist.

-km

[1] Strictly speaking, Kemeny is an estimator connected to a function
that processes the estimate. The estimate is the consensus ordering and
the function returns the candidate on top of that estimate ordering as
the best fit to the electorate.