# [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