Markus wrote: Dear participants, due to Condorcet, a "proposition" is a statement of the form: "X is better than Y." An "opinion" is a set of n*(n-1)/2 propositions (one for each pair of candidates). I reply: Did Condorcet say that there have to always be n(n-1)/2 propositions, and that a proposition has to say one candidate is better than another? Suppose that, initially, there's a pairwise tie. Then, if Condorcet said what you claim, then initially there's no opinion, if an opinion must have n(n-1)/2 propositions, and a proposition must say that one candidate is better than another. So are you making the silly claim that when there's a pair-tie, then initially there's no opinion at all? In fact, then there can never be an opinion, unless you also believe that Condorcet wanted us to write an X>Y opinion when there isn't one. There are 2 less absurd conclusions. Maybe a proposition can also say X=Y. Or maybe, if a proposition must say X>Y, then we can have fewer than n(n-1)/2, for the atypical case where there are 1 or more pair-ties. Your claim leads to the asinine conclusion in the paragraph before last, and also requires the equally asinine conclusion that "eliminate" must mean "reverse", and doesn't really mean "eliminate". What English dictionary are you using. Would you mind quoting to us its definition of "eliminate"? Or, better yet would be if you have a dictionary for the French in Condorcet's period, and could tell us how that dictionary translates the French word that has been translated as "eliminate". Mike Ossipoff A "possible opinion" is a set of n*(n-1)/2 propositions (one for each pair of candidates) that is compatible to a ranking. An "impossible opinion" is a set of n*(n-1)/2 propositions (one for each pair of candidates) that is incompatible to every ranking. Due to Condorcet, when one "eliminates" a proposition of an opinion then one still has an opinion. Therefore, it is clear that "eliminating" can only mean "inverting". Markus Schulze _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com
