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<div class="moz-cite-prefix">On 05/04/2022 10:22, Richard Lung
wrote:<br>
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<blockquote type="cite"
cite="mid:a41592ab-e646-61ce-dc0b-6cbd71274532@ukscientists.com">
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<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Even in a highly contrived test election, that
didn’t allow much margin for error, the two most rational
systems agreed on the result.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">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.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Richard Lung.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""><br>
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<div class="moz-cite-prefix">On 04/04/2022 12:32, Kristofer
Munsterhjelm wrote:<br>
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<blockquote type="cite"
cite="mid:5c89ebbe-d621-ea23-8515-0d3bf847114c@t-online.de">
<pre class="moz-quote-pre" wrap="">On 03.04.2022 11:54, Richard Lung wrote:
</pre>
<blockquote type="cite">
<pre class="moz-quote-pre" wrap="">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.
</pre>
</blockquote>
<pre class="moz-quote-pre" wrap="">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.
</pre>
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