Norman Petry wrote:
> On 5 Mar 2000 Bart Ingles wrote:
>
> >Adding a 'random society' component to the model would increase the
> >probability of cycles. It looks like a purely random model reaches 50%
> >at around 10 or 11 candidates (it would still take many more to reach
> >the figure shown above, though).
>
> Bart didn't give a source, but I think I heard somewhere that this statistic
> was from some of Duncan Black's writings. [...]
FWIW, I got it from Merrill (1988), Tables 2.1 and 2.2, given as part of
the background for Condorcet efficiency simulation results.
Using spatial models with two and four dimensions, 98+% of elections had
Condorcet winners. With the purely random model (voter rankings
generated from random utilities, not randomly generated matrices), the
5-candidate figure was around 76%.
-B