Dear Blake, I could simplify your 7 July 2000 example to 7 candidates: AC 20 AD 30 BA 60 CB 22 CD 11 DB 32 DE 16 EC 10 EF 42 FG 43 GE 44 SD chooses candidate C. If "DE 16" is changed to "DE 9" then SD chooses candidate D. Markus Schulze schulze at sol.physik.tu-berlin.de schulze at math.tu-berlin.de markusschulze at planet-interkom.de