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<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">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.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Laplace</span><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold""> had a
metaphysical belief in determinism. (That is an interesting
hypothesis, as
Bonaparte commented.) Yet his adjudication between Condorcet and
Borda appeared
in his treatise on probability. Elections are a statistic. (I
follow the
account by JFS Ross, in Elections and Electors.)</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Laplace</span><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold""> had the first and
perhaps the last word on Condorcet pairing or Round Robin
elections: they don’t
take into account the relative importance of preferences.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Over
a century later, in the 1940s, this message was reinforced, by
SS Stevens on
scales of measurement. Judging winners solely by binary
elections, staying at
the least powerful, nominal scale of measurement, leaves out a
comparison of
the whole range of candidates, at once, that is to say, an
ordinal scale of measurement,
which preference voting is the next, more powerful scale. It is
the difference
between absolute, all or nothing choice, of a single order of
preference, and
the relative choice of a whole range of preferences.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Condorcet
pairing may occasionally contradict preference voting. But this
cross-check
never departs from minimal choices, which do not justify a veto
over the more
general relative choice of preference voting.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Moreover,
a case in about 135, like </span><span style="font-size:
14.0pt;font-family:"Arial Rounded MT Bold"">Burlington</span><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold""> is not
statistically significant enough, to inaugurate Condorcet
pairing as an arbiter
in (preferential) elections, considered as statistical
estimates.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold""> </span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">After
the nominal and ordinal scales, Stevens progresses to the
successively more
powerful interval scale and ratio scale. These are both
proportional measurements.
The only difference is that the interval scale lacks a real
zero. An example is
the conventional temperature scales like Fahrenheit and
centigrade. Their
different zero points on the scale are a matter of convention,
such as making
zero, when water freezes (either in salt water or fresh-water).</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">The
quota is an example of a ratio scale. Party lists, however are a
particular
vote in a general election. Likewise, the local constituency
vote in a national
election. The Andrae or Hare system are the more logical general
vote in a
general election. The interval scale appears in voting method,
in surplus or
deficit of a quota, which sets its conventional level of zero. A
candidate
whose votes exactly equal the quota has a zero surplus and a
zero deficit of votes.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">The
transferable vote possesses all four scales of measurement; a
rare quality in
voting methods, which I have long since argued qualifies it as
something like
scientific method of elections.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Regards,</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Richard Lung.<br>
</span></p>
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<div class="moz-cite-prefix">On 02/04/2022 10:51, Kristofer
Munsterhjelm wrote:<br>
</div>
<blockquote type="cite"
cite="mid:4e6fcabf-df29-39b7-6a06-05fa4d5e56e5@t-online.de">
<pre class="moz-quote-pre" wrap="">On 25.03.2022 20:50, Richard Lung wrote:
</pre>
<blockquote type="cite">
<pre class="moz-quote-pre" wrap="">
I can't help but think that this group is absorbed in determining
election winners, rather than representatives of the people, as in a
democracy.
</pre>
</blockquote>
<pre class="moz-quote-pre" wrap="">
For me at least - I don't know if that's why others are focusing on
single-winner - it's because multi-winner is so much harder, it's
difficult to see even where to begin to prove anything.
Take Droop proportionality, for instance. It is known that party list
methods that are based around fulfilling a quota criterion must fail
what's called population pair monotonicity (or the Alabama paradox); and
Droop proportionality implies a sort of one-sided quota criterion, call
it a lower quota.
But is then Droop proportionality compatible with population pair
monotonicity? Is it only so for methods that reduce to D'Hondt (which
passes a lower quota property)? I don't know. Or perhaps population pair
monotonicity is the analog of the participation criterion, which almost
all voting methods fail anyway, and thus is not something we need to pay
attention to.
There are many questions like this. Another one is (strong
seat-independent) summability: we know of a bunch of methods that are
summable for single-winner. But is it even possible to pass both Droop
proportionality and summability for a general ranked voting method?
Again, very difficult to prove *or* disprove. I have been playing with
this on and off, and I suspect it is impossible. But I also suspected
that the combination (for single-winner) of monotonicity and DMTBR was
impossible, and I was at least partially shown wrong by my optimal
strategy solver.
The cardinal voting camp has probably been more successful, but they
have the benefit of being able to treat ballots numerically. Trying to
do so with ordinal ballots usually leads to clone dependence, Condorcet
failure or similar problems.
There's also an argument that the best representatives of the people are
a representative sample of the people, i.e. that one should not elect at
all, but just populate the representative body with an unbiased
selection of all kinds of people who make up society. If so, then
large-scale PR is "solved" by removing the need to solve it by elections
in the first place. On the other hand, this might also make the question
of a good single-winner method moot as well, since parliamentary
procedure is usually very simple.
That's not to say I've been completely uninterested in multi-winner. My
first post here showed tradeoffs between proportionality (in a simple
yes-no model) and total satisfaction: to some degree, if you please each
faction more, you end up pleasing all of society less as the faction
representatives become more polarized.
<a class="moz-txt-link-freetext" href="https://munsterhjelm.no/km/elections/multiwinner_tradeoffs/">https://munsterhjelm.no/km/elections/multiwinner_tradeoffs/</a> Which might
be an obvious result in retrospect, but the gap between social optimum
and known methods shows that there's potentially a lot more improvement
to be had.
I also devised MCAB, which is a more strategy resistant variant of EAR
or the Bucklin transferable vote:
<a class="moz-txt-link-freetext" href="https://electowiki.org/wiki/Maximum_Constrained_Approval_Bucklin">https://electowiki.org/wiki/Maximum_Constrained_Approval_Bucklin</a>
-km
</pre>
</blockquote>
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