Here's a useful cycle proof condition that we used in step three of my previous message under the topic "tanking advantage ...":)
If there are 2n levels, and only those comparisons that involve a difference of n or more levels are used, then there can be no pairwise beat cycle. Proof: The above condition is more stringent than allowing all comparisons between levels from the upper half with levels in the lower half, and this weaker condition is equivalent to placing an approval cutoff between the middle two levels, which in turn is strong enough to prevent cycles, because pairwise approval comparisons do not cycle. Forest ---- Election-Methods mailing list - see http://electorama.com/em for list info
