Perhaps Tengvall thinks of penalizing clones as a form of discouraging or repelling clones, so that his clone punishing method has more of a tendency to get rid of clones than a clone independent method, and therefore more deserving of the description "clone free."
Forest On Mon, 13 Oct 2003, Markus Schulze wrote: > Hallo, > > there was a discussion between Arto Tengvall (the specialist > on election methods of the "Leader of the Free World" > project) and me about which election method should be used > at the LFW project. I posted my paper "A New Monotonic > and Clone-Independent Single-Winner Election Method" > (http://groups.yahoo.com/group/election-methods-list/files/nmciswem.pdf) > to him. Arto Tengvall replied (10 Oct 2003): > > > About the Leader of the World - project. > > > > There will be one official electoral result, counted by the very > > best method known so far. Today, it is my method, but if someone > > can show that there is another method still better (judged by > > essential mathematical and logical criteria), I would have no > > objection against changing the method. Here is a short and easy > > definition of my method. As you can see, it also satisfies the > > criteria you have used yourself. It satisfies some extra criteria, > > too, which I have no time to write now. > > > > 1. Count votes in all pairwise comparisons, according to this: > > Count a vote to X from every ballot where X is given better or > > equal preference than Y, and to Y from every ballot where Y is > > given better or equal preference than X. X beats Y if the former > > score is bigger than the latter, and vice-versa. > > > > 2. The vote minimum of each X is the smallest score of X in any > > of X:s comparisons. > > > > 3. There is a beatpath from X to Y if X beats Y (in pairwise > > comparison between these two) or X beats some Z that beats Y. > > > > 4. Eliminate every candidate X such that there is a beatpath > > from some Y to X but not vice-versa. > > > > 5. Check the vote minimum of each non-eliminated. The winner > > is the one with the biggest vote minimum. (A tie is possible.) > > In short: The Tengvall winner is that Schwartz winner A whose > worst pairwise comparison with another candidate B (measured > by the absolute number of voters who strictly prefer candidate B > to candidate A) is minimal. > > When every voter casts a complete ranking then Tengvall's method > is identical with Schwartz//MinMax. > > On first view, Tengvall's method seems to be identical with > Schwartz//MinMax(VotesAgainst). But when the strength of a > pairwise comparison is measured by the absolute number of > voters who strictly prefer candidate B to candidate A then > it isn't guaranteed that the worst pairwise comparison > of the Schwartz winner A with another candidate is necessarily > with another Schwartz winner. Therefore, Tengvall's method > isn't quite Schwartz//MinMax(VotesAgainst). > > I wrote to Tengvall, that his method violates independence of > clones and reversal symmetry. And I asked him which criteria > he uses to conclude that his method is the very best method > known so far judged by essential mathematical and logical > criteria. Arto Tengvall replied (13 Oct 2003): > > > My method has similarities with Schwartz//Minmax, however one > > defines that method. I have seen many different definitions > > but my method is a little bit different. Maybe you should > > look again, without thinking Schwartz method, so without any > > pre-opinions. Then you can see, withaout any deeper analysis, > > that my method easily fullfills clone-independency and reversal > > symmetry. > > Can somebody tell me where I have made a mistake? > > Markus Schulze > ---- > Election-methods mailing list - see http://electorama.com/em for list info > ---- Election-methods mailing list - see http://electorama.com/em for list info
