Jameson wrote: > I can show (under reasonable strategic assumptions) that my delegated > system SODA elects one of the candidates who beats all with a winning vote > beatpath of length 2 or less, if there is any such candidate. "A beats B > with a winning vote beatpath of length 2" means: there is some C such that > the minimium of (votes for A against C, votes for C against B) is greater > than votes for B against A. > Obviously, if we allow any length of beatpath, and if there are no ties, > there must be some beats-all winner. But is it possible that there is no > winner with beatpaths of length 2 or less? Can anybody give an example of > such an electorate? If I understand you correctly, this electorate does what you want: 29:A>C>B>D 15:B>D>A>C 16:D>C>B>A If beatpaths of all lengths are considered, as in the Schulze method, A loses no beatpath comparisons. In particular, the beatpath A>C>B>D is stronger than D>A. But A needs a beatpath that long to defeat D; the beatpaths A>B>D and A>C>D are weaker than D>A. Using only beatpaths of length 2 or less, every candidate loses a beatpath comparison. What would strategic SODA do in the above case? -- Rob LeGrand rob@approvalvoting.org