I found it somewhat difficult to follow, but is it true that if there are no pairwise ties the Smith and Schwartz sets are identical?
Markus Schulze said: > suppose "d[X,Y]" with X<>Y is the number of voters who > strictly prefer candidate X to candidate Y. Then the > "Smith set" is the smallest non-empty set of candidates > with d[A,B] > d[B,A] for each candidate A of this set > and each candidate B outside this set. > > A "chain from candidate A to candidate B" is an ordered > set of candidates C(1),...,C(n) with the following three > properties: > > 1. C(1) is identical to A. > 2. C(n) is identical to B. > 3. d[C(i),C(i+1)] - d[C(i+1),C(i)] > 0 > for each i = 1,...,(n-1). > > A "Schwartz winner" is a candidate A who has chains at > least to every other candidate B who has a chain to > candidate A. The "Schwartz set" is the set of all Schwartz > winners. > > The term "innermost unbeaten set" is another term for > "Schwartz set." > > Example: Suppose that there are 3 candidates; candidate A > pairwise beats candidate B; candidate B pairwise beats > candidate C; and there is a pairwise tie between > candidate A and candidate C. Then the Smith set > is ABC and the Schwartz set is A. ---- Election-methods mailing list - see http://electorama.com/em for list info
