A note on scoring rules that respect majority in choice and elimination

In a recent paper [Mathematical Social Sciences 43 (2002) 151], M.R. Sanver investigates scoring rules for social choice problems with n voters and m alternatives. He proves that unless n{2, 3, 4, 6, 8} a scoring rule cannot simultaneously respect majority in choice and majority in elimination. In this short technical note, we first point out a serious flaw in Sanver’s proof. Then we provide a complete proof for a corrected version of Sanver’s statement: Unless n{2, 3, 4, 5, 6, 8, 10, 12} a scoring rule cannot simultaneously respect majority in choice and majority in elimination