*To*: debian-vote@lists.debian.org*Subject*: Re: Constitutional amendment: Condorcet/Clone Proof SSD vote tallying*From*: Markus Schulze <markus.schulze@alumni.tu-berlin.de>*Date*: Fri, 23 May 2003 11:20:18 +0200*Message-id*: <3ECDE7D2.E465BB53@alumni.tu-berlin.de>

Hallo, it is necessary to distinguish between the participation criterion and the monotonicity criterion. The participation criterion says that a set of additional voters who strictly prefer candidate A to candidate B must not change the winner from candidate A to candidate B. The Condorcet criterion and the participation criterion are incompatible (Herve Moulin, "Condorcet's Principle Implies the No Show Paradox," Journal of Economic Theory, vol. 45, pp. 53-64, 1988). Therefore, this criterion is _of no concern_ when we want to discuss which Condorcet method should be adopted. The monotonicity criterion says that (1) when some voters rank a given candidate A higher without changing the orders in which they prefer the other candidates then candidate A must not be changed from a winner to a loser and (2) when some voters rank a given candidate A lower without changing the orders in which they prefer the other candidates then candidate A must not be changed from a loser to a winner. It is _not_ true that the monotonicity criterion implies the participation criterion. It is also _not_ true that the monotonicity criterion implies that when candidate A is the original winner then adding voters who strictly prefer candidate A to every other candidate must not change candidate A into a loser. Suppose that candidate A is the original winner. Suppose that an ABC voter is added. Then on the one side this voter is changed from a voter who ranks all three candidates equally to a voter who strictly prefers candidate A to every other candidate; therefore, one could expect that the monotonicity criterion implies that candidate A stays the winner. However, this voter is also changed from a voter who ranks candidate B and candidate C equally to a voter who strictly prefers candidate B to candidate C. Therefore, the requirement that the orders in which the other candidates are prefered aren't changed isn't met. However, it is true that the monotonicity criterion implies that when candidate A is the original winner then adding voters who strictly prefer candidate A to every other candidate and who rank all the other candidates equally must not change candidate A into a loser. Markus Schulze

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