STAR
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.)
On Monday, 14 August 2023 at 00:14:16 BST, Kristofer Munsterhjelm km_elmet@t-online.de wrote:
On 8/14/23 00:33, Toby Pereira wrote:
To be clearer I should have said "logical impossibility" rather than
"logical fallacy".
Is it a logical impossibility, though? The Condorcet jury theorem may be
unrealistic, but it's not a self-evident contradiction.
-km
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.
CJC
On 14/08/2023 09:02, Toby Pereira wrote:
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.)
On Monday, 14 August 2023 at 00:14:16 BST, Kristofer Munsterhjelm
km_elmet@t-online.de wrote:
On 8/14/23 00:33, Toby Pereira wrote:
To be clearer I should have said "logical impossibility" rather than
"logical fallacy".
Is it a logical impossibility, though? The Condorcet jury theorem may be
unrealistic, but it's not a self-evident contradiction.
-km
For what it's worth, my understanding of Condorcet's line of thought is
this:
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.
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.
Having fallen into contradiction, he decided to stick with his
criterion, but without any serious justification that I can see.
CJC
On 14/08/2023 09:07, Colin Champion wrote:
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.
CJC
On 14/08/2023 09:02, Toby Pereira wrote:
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.)
On Monday, 14 August 2023 at 00:14:16 BST, Kristofer Munsterhjelm
km_elmet@t-online.de wrote:
On 8/14/23 00:33, Toby Pereira wrote:
To be clearer I should have said "logical impossibility" rather than
"logical fallacy".
Is it a logical impossibility, though? The Condorcet jury theorem may be
unrealistic, but it's not a self-evident contradiction.
-km
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