# [EM] CIVS cycles data

Warren Smith wds at math.temple.edu
Sun Sep 4 16:04:15 PDT 2005

```>On 9/2/05, Andrew Myers <andru at cs.cornell.edu> wrote:
> I thought the folks on this list would find it interesting to see
> some actual empirical data on how often cycles happen. I have data on
> 99 CIVS elections that have been run in which more than 10 voters
> participated (max was 1749) and in which there were at least three
> candidates
> (max was 72). These 99 elections break down as follows:
>
> had a Condorcet winner: 85
>
> no Condorcet winner, but a unique unbeaten candidate: 7
>    [i.e. is unique guy who would be a CW if got epsilon more]
>
> multiple unbeaten candidates in real ties: 3
>    [i.e. is a set of tied winners]
>
> real cycles requiring completion: 4
>
> These results suggest to me that the concern about cycles arising in
> Condorcet methods is a bit excessive.

--Aha.  Well now I know that CIVS means
http://www5.cs.cornell.edu/~andru/civs/,
I am now more worried - I do not know how many of those CIVS elections
were "real" elections and how many were kind of unreal demos, or
for things nobody really cared about, or something.

Another thing is, your results give a large range of uncertainty on how rare cycles
are.  That is because of ties.  You had a lot more ties (7+3=10) than cycles (4).
In a large election, there would not be ties.  So with enlargement, your cases
with ties might in some cases become cycles.   So I'm thinking your
results show the fraction of the time you
get cycles is somewhere between 4/99 and 14/99, plus there is uncertainty of
around +-4 in that "14", plus there is the question of how 'real' your elections
were, which might mean your sample is biased versus real elections.

That is ok - the range "0 to 20%" is still worthwhile information - but it
is rather less precise that I would have hoped.  It might well be the answer is
"5% of (>=3)-candidate condorcet elections involve cycles" (and based on your data that
would be my most-likely guess) but I am not confident.

wds

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