Hallo, Eric Maskin, a Nobel laureate, is currently very active in promoting the Black method. The Black method says: If there is a Condorcet winner, then the Condorcet winner should win; if there is no Condorcet winner, then the Borda winner should win.
See e.g.: 1 Sep 2009: http://research.microsoft.com/apps/video/default.aspx?id=143268 8 Apr 2011: http://www.youtube.com/watch?v=Bx_lt06W9Ww Maskin argues as follows: If election method X is the best possible election method in domain X and if election method Y is the best possible election method in domain Y and if domain X and domain Y are disjoint and if domain X and domain Y together cover all possible situations, then the best possible election method is to use election method X in domain X and election method Y in domain Y. Maskin argues: "domain X" = "situations with a Condorcet winner"; "election method X" = "any Condorcet method"; "domain Y" = "situations without a Condorcet winner"; "election method Y" = "Borda method". *********************************** That method, that uses election method X in domain X and election method Y in domain Y, will be called "election method Z". *********************************** Maskin's argumentation doesn't work because of the following reason: Whether an election method is good or bad depends on which criteria it satisfies. Most criteria say how the result should change when the profile changes. Now it can happen that the original profile and the new profile are in different domains. This means that, to satisfy some criterion, election method X for domain X and election method Y for domain Y must not be chosen independent from each other. Example: The participation criterion says that adding some ballots, that rank candidate A above candidate B, must not change the winner from candidate A to candidate B. Election method X satisfies the participation criterion in domain X. Reason: If candidate A was the winner in the original profile and if the original profile was in domain X, then this means that candidate A was the Condorcet winner and, therefore, that candidate A pairwise beat candidate B. If candidate B is the winner in the new profile and if the new profile is in domain X, then this means that candidate B is the Condorcet winner and, therefore, that candidate B pairwise beats candidate A. If candidate A pairwise beat candidate B in the original profile and if candidate B pairwise beats candidate A in the new profile, then this means that the added ballots rank candidate B above candidate A. Election method Y satisfies the participation criterion in domain Y, because the Borda method satisfies the participation criterion in general. However, election method Z doesn't satisfy the participation criterion since the Condorcet criterion and the participation criterion are incompatible. In short: Even if election method X satisfies criterion A in domain X and election method Y satisfies criterion A in domain Y, it doesn't mean that election method Z satisfies criterion A. Therefore, Maskin's argumentation doesn't work. *********************************** I also question the claim that the Borda method is the best possible election method in situations without a Condorcet winner. Markus Schulze ---- Election-Methods mailing list - see http://electorama.com/em for list info
