[EM] Richard Moore's idea continued

[Forest Simmons]

On Sat, 26 Apr 2003, Forest Simmons wrote:

>
> In practice when the probability calculations are too long or complicated,
> the winning social ordering can be determined by Monte Carlo simulation,
> using many randomly chosen test vectors until the desired level of
> certainty about which ordering is most likely to agree with the majority
> in the long run is established, according to established principles of
> probability and statistics.
>

When the number of candidates is not too large, a sufficient set of test
vectors would be the set of all differences of vectors between permutation
vectors (i.e. the vectors representing various possible rankings),
normalized to unit length.  Of course when two or more such vectors turn
out to be parallel or anti-parallel, all after the first are redundant.

In the case of three candidates, six vectors suffice, even though there
are 30 distinct non-zero vectors that are the differences of the six
permutation vectors.

Forest