Re: [EM] Winners or representation?
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.
On 05.04.2022 19:56, Richard Lung wrote:
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.
That doesn't seem to be related to either single- vs multi-winner or the
nonexistence/coherence of voting method criteria. It's more related to
IIA and rock-paper-scissors elections.
Would you say that my estimator analogy makes sense and shows that
election criteria can exist and be coherent?
-km