Dear Craig, here is the published version of my paper: http://www.mcdougall.org.uk/VM/ISSUE17/I17P3.PDF
Here is the extended version of my paper: http://groups.yahoo.com/group/election-methods-list/files/schulze1.zip You wrote (29 Jan 2005): > The words "strictly prefer" are undefined. That is a major problem. In the published version of my paper, I write that I presume that each voter casts a partial ranking of all candidates. In the extended version of my paper, I give a very detailed definition for "partial rankings". I write: > It is presumed that each voter casts a partial (i.e. a not necessarily > complete) ranking of all candidates. Suppose (1) "A >v B" means "voter > v strictly prefers candidate A to candidate B" and (2) "A =v B" means > "voter v is indifferent between candidate A and candidate B". Then > voter v casts a partial ranking when the following six conditions > are satisfied. > > 1. For each pair of candidates A and B exactly > one of the following three statements is true: > A =v B, A >v B, B >v A. > 2. A =v A for every candidate A. > 3. ( A >v B and B >v C ) => A >v C. > 4. ( A =v B and B >v C ) => A >v C. > 5. ( A >v B and B =v C ) => A >v C. > 6. ( A =v B and B =v C ) => A =v C. > > However, it is not presumed that each voter casts a complete > ranking. A complete ranking is a partial ranking with the following > additional property: > > 7. A and B are not identical. => ( A >v B or B >v A ). > > Therefore, a possible way to implement the proposed method is to > give to each voter a complete list of all candidates and to ask each > voter to rank these candidates in order of preference. The individual > voter may give the same preference to more than one candidate and he > may keep candidates unranked. When a given voter does not rank all > candidates then it is presumed that this voter strictly prefers all > ranked candidates to all not ranked candidates and that this voter > is indifferent between all not ranked candidates. You complain that I call this binary relation "strictly prefer". However, how I call this binary relation is of no concern as long as the above properties are satisfied. Please read: http://alumnus.caltech.edu/~seppley/Set%20Operators%20and%20Binary%20Relations.htm ************* You wrote (29 Jan 2005): > Mr Schulze didn't mention tests that didn't pass his method. Already in the published version of my paper, I mention that my method violates participation, mono-add-top, mono-remove-bottom, later-no-help, and later-no-harm. Furthermore in the extended version of my paper, I mention that my method also violates consistency, mono-raise-random, mono-sub-top, mono-raise-delete, mono-sub-plump, and independence from Pareto-dominated alternatives and that it doesn't guarantee that the winner is always chosen from the uncovered set. Markus Schulze ---- Election-methods mailing list - see http://electorama.com/em for list info
