[EM] First Condorcet cycle ever spotted in a national presidential election (!?! apparently)
seppley at alumni.caltech.edu
seppley at alumni.caltech.edu
Fri Dec 11 13:45:12 PST 2009
Jameson Quinn misinterpreted what I wrote. He claimed I described a random
elections model. I described a scenario where 3 candidates are very
similar, which is not the same as utter randomness.
Assuming the votes in all three pairings are very close to 50%--which
would be expected if the 3 candidates are very similar--I think the chance
of a majority cycle is nearly 25%, since there are 8 combinations of
pairwise results, and 2 of the 8 are cyclic: [A>B, B>C, C>A] and [B>A,
C>B, A>B].
(I should have worked that out before posting my previous message, which
wrongly suggested the chance of a cycle would be nearly 50%.)
Regards,
Steve
-----------------------------------------------
> 2009/12/9 seppley <seppley at alumni.caltech.edu> wrote:
>> Without studying details of the three Romanian candidates and the
>> voters'
>> preferences, the explanation of this majority cycle cannot be known for
>> sure.
>>
>> However, consider a case of three very similar candidates. The voters'
>> preferences in each of the three possible pairings would be nearly tied
>> (approximately 50% preferring each candidate over each other candidate).
>> In such a case, a cycle involving three small majorities would not be
>> rare. Almost an even bet?
Jameson Quinn wrote:
> Not rare, you're right. However, what you are describing is essentially
> something like a "random elections model" or perhaps a "Dirchlet model",
> which, according to WDS's table of
> calculations<http://rangevoting.org/Romania2009.html>,
> for 3 or 4 serious candidates, have probabilities of Condorcet cycles
> somewhere in the range of 6-18% - which is certainly nothing to be shocked
> about when it happens by chance, but also a good deal less than an even
> bet.
>
>> --Steve
>> --------------------------
>> Jameson Quinn wrote:
>> > This is good math, and very interesting, but it doesn't speak at all
>> about
>> > the politics of the matter. Have you figured out any tentative
>> explanation
>> > for the Condorcet cycles you postulate? Why would, for instance, O>B>G
>> > voters be more common than O>G>B voters, yet in the mirror-image
>> votes,
>> > B>G>O voters more common than G>B>O ones? (I realize that the
>> Condorcet
>> > cycle does not require exactly that circumstance, but it suggests%
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