71.234.188.145: Impossibility of "Fair" Tie-breaker? (2010-04-15 18:52) [#7639]

Bob McGuigan: The work of Kenneth Arrow in social choice theory says that under certain reasonable conditions there is no fair way to make a societal ranking of alternatives from individual rankings. See this Wikipedia article for more information. Breaking ties isn't the same sort of thing but Condorcet's paradox, the problem that leads to Arrow's result, also is seen in tournament results. For example, in a round robin tournament with eight players suppose players A, B, and C are all tied for first place with the same won/lost scores of 6 - 1. Suppose further that A defeated B, B defeated C, and C defeated A and A, B, and C won all their games except the losses already specified. This creates the Condorcet condition and it seems that none of the formal tiebreaking methods based only on performance in the tournament will break this tie. In this sort of situation it seems fairest to me to have co-champions and to split the prizes.