Dear Forest Simmons, I wrote (16 Feb 2005): > 1. Please post an authoritative definition for the > "Dutta set"! (Please post one that doesn't presume > that there are no pairwise ties!) > > 2. Please post an authoritative definition for > "Condorcet lottery"! (As far as I remember correctly, > Jobst Heitzig wrote that "Condorcet lottery" is not > monotonic. So it seems that Jobst Heitzig and you > are talking about slightly different things.)
You wrote (16 Feb 2005): > Markus asked me to define the Dutta Set, the Condorcet > Lottery method, and clarify whether or not this lottery > method is monotonic. > > I think the best I can do is to include a copy of Jobst's > posting of 5 Jan 2005, which answers all of these questions > to one degree or another. > > In particular, the monotonic nature of the method is > described in properties 11 and 12 below. Thank you for forwarding Jobst's mail. As far as I understand his mail correctly, then Condorcet lottery is not monotonic in the general case. He wrote: "Although the method is monotonic in the sense of 11. and 12., the probability p(x) can still decrease when x is reinforced and there are more than 5 candidates." Also Jobst's mail doesn't contain a definition for Dutta's minimal covering set. Markus Schulze ---- Election-methods mailing list - see http://electorama.com/em for list info