# [EM] Winners or representation?

Richard Lung voting at ukscientists.com
Tue Apr 5 10:56:54 PDT 2022

```On 05/04/2022 10:22, Richard Lung wrote:
>
> Thru-out the world of academe, from the American Mathematical Society
> to innumerable social choice classes, can or could be found examples
> of how about five different single-member voting systems all produce
> different results. This is held to demonstrate a theorem of the
> Impossibility of determining a winner.
>
> The example by Paulos, in his numeracy dictionary, really only showed
> that different amounts of information, given by the vote, and used in
> the count, produce different results. Unsurprisingly – to me, anyway.
> One of the methods used was Condorcet pairing. All you had to do was
> modify it, with the standard statistical technique of weighting in
> arithmetic proportion, and that example gives the same result, for
> weighted Condorcet pairing, as the Borda count.
>
> Even in a highly contrived test election, that didn’t allow much
> margin for error, the two most rational systems agreed on the result.
>
> This perhaps shows the credulity towards a deterministic theorem being
> proved by different election statistics, with different margins of
> error, from different inputs of preferential information.
>
> This brings me back to how STV can be made extra rational with a
> binomial STV, even more fully in accord with the widely accepted
> scales of measurement, from SS Stevens.
>
> Richard Lung.
>
>
> On 04/04/2022 12:32, Kristofer Munsterhjelm wrote:
>> 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.
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