Dear Forest! Big Sorry for not having read carefully enough. I missed the point about public elections not being supposed to show much symmetry. That is a very good point I guess which we could even strengthen to this claim:
---- In almost all public elections, there will either be a CW or a 3-cycle so that each other candidate is beaten by at least 2 of the 3. ---- Do you agree? When we assume this, you are perfectly right to suggest to use a two-step method which first reduces to Dutta's minimal covering set (=the above-mentioned CW or 3-cycle) and then defines an efficient lottery on the 3 candidates, for example using the wonderfully simple Random Ballot method. So, YES, I think that Random Ballot Dutta is a very good approach -- good work! Now we could even try to include some preference strength information, for example like this: a) Voters specify an approval cutoff. Determine the Dutta set D. Draw a random ballot and remove all elements of D which are not approved on that ballot, except when no element of D is approved. Repeat drawing random ballots until only one element remains. b) Or like this: Voters specify ratings and defeat strengths s(X>Y) are computed as in Cardinal Weighted Pairwise. In the Dutta set X>Y>Z, give X a probability proportional to s(X>Y)/s(Z>X). c) Or any other way :-) Yours, Jobst PS: One minor point: We should justify the "public elections" claim a bit further since it might collide with a similar but contradictory assumption from tournament theory I referred to yesterday. The claim is that in a tournament with a sufficient number of almost equally good teams, it can be expected that none of the teams is covered and no set of teams is a proper clone set. Or to put it otherwise: If we assume that it is equally likely that X>Y and that Y>X no matter how the defeats come out between other pairs, then there will most likely be no clones and no covered candidates. It would be interesting to know whether in such a "random tournament" also the Dutta set must be expected to consist of all candidates... __________________________________________________________ Mit WEB.DE FreePhone mit hoechster Qualitaet ab 0 Ct./Min. weltweit telefonieren! http://freephone.web.de/?mc=021201 ---- Election-methods mailing list - see http://electorama.com/em for list info
