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<font face="Helvetica, Arial, sans-serif">For what it's worth, my
understanding of Condorcet's line of thought is this:<br>
</font><br>
<font face="Helvetica, Arial, sans-serif"><font face="Helvetica,
Arial, sans-serif"><font face="Helvetica, Arial, sans-serif">He
started from his jury theorem, which asserts (truly) that if
more voters prefer A to B than prefer B to A in a two-way
ballot, then A is likelier than B to be the best choice. He
extended this to m-way ballots concluding that if there is a
Condorcet ranking (i.e. a ranking in which each candidate
beats each following candidate), then this ranking is the
likeliest to be the true one. This is where he needed an
independence assumption; I believe that his result is false. <br>
He then noticed that maximum likelihood was the wrong
approach, and that marginalisation would be better. In other
words, what matters is not whether A is the head of the
likeliest ranking, but whether the total probability of all
rankings headed by A is greater than the total probability of
all rankings headed by any other candidate. He concluded that
the Condorcet winner did not have this property (and here he
was right). Black gives a numerical example. I think there are
several errors in Condorcet's reasoning, but he was ahead of
his time in preferring marginalisation to maximum likelihood.
<br>
Having fallen into contradiction, he decided to stick with
his criterion, but without any serious justification that I
can see.<br>
<br>
CJC<br>
<br>
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<div class="moz-cite-prefix">On 14/08/2023 09:07, Colin Champion
wrote:<br>
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cite="mid:eeeef276-62b4-0fcf-6504-68b534c9a47b@routemaster.app">
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<font face="Helvetica, Arial, sans-serif">I think it would be
perfectly reasonable to accuse Condorcet of contradiction - not
in his jury theorem, but in its generalisation to m-way voting.
In order to apply his jury theorem to general voting problems,
Condorcet had to assume that A's being better than C was
independent of A's being better than B and B's being better than
C.<br>
<br>
CJC<br>
</font><br>
<div class="moz-cite-prefix">On 14/08/2023 09:02, Toby Pereira
wrote:<br>
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cite="mid:898596557.4576794.1692000178435@mail.yahoo.com">
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<div dir="ltr" data-setdir="false">I wasn't referring to the
Condorcet Jury Theorem. I was referring to the fact that
there's no way that you can consistently define society's
preference in a way that you can determine whether society
prefers A or B by looking at the pairwise comparison.
(Because of the possibility of cycles.)</div>
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<div> On Monday, 14 August 2023 at 00:14:16 BST, Kristofer
Munsterhjelm <a class="moz-txt-link-rfc2396E"
href="mailto:km_elmet@t-online.de"
moz-do-not-send="true"><km_elmet@t-online.de></a>
wrote: </div>
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<div dir="ltr">On 8/14/23 00:33, Toby Pereira wrote:<br
clear="none">
> To be clearer I should have said "logical
impossibility" rather than <br clear="none">
> "logical fallacy".<br clear="none">
<br clear="none">
Is it a logical impossibility, though? The Condorcet
jury theorem may be <br clear="none">
unrealistic, but it's not a self-evident contradiction.
<div class="ydp148eb332yqt9332482924"
id="ydp148eb332yqtfd11691"><br clear="none">
<br clear="none">
-km<br clear="none">
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