[EM] STAR

[Colin Champion]

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 at 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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