Here's a cyclic ambiguity (a five-way circular tie) to try with various voting systems: 5: ABCDE 6: BCDEA 7: CDEAB 8: DEABC 9: EABCD
So A>(B, C), B>(C, D), C>(D, E), D>(A, E), and E>(A, B). You could also look at 5: ACEBD 6: BDACE 7: CEBDA 8: DACEB 9: EBDAC where A>(C, E), B> (A, D), C>(B, E), D>(A, C) and E>(B, D) The diagrams of these circular ties look like a pentagram, which is kind of cool. Within these two diagrams you could also mix up the relative strengths (56789, 65798, 75967, etc) to see where various voting methods differ. Any ideas on how Saari would unravel the ties? Michael Rouse [EMAIL PROTECTED] ----- Original Message ----- From: <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Friday, March 29, 2002 8:03 AM Subject: RE: Saari and Cyclic Ambiguities > Alex wrote in part- > > Saari pointed out that cyclic ambiguities come from a "Condorcet profile" > > or "symmetric profile". If the electorate consists of 3 groups > > > 35 A>B>C > > 33 B>C>A > > 32 C>A>B > > > we can "decompose" the electorate into > > > 32 A>B>C + 3 A>B>C > > 32 B>C>A + 1 B>C>A > > 32 C>A>B > ---- > D- Selectively ignoring ANY votes in my local area is STILL a major election > felony. > > Who has a YES majority ??? > > Saari can appear at any time on this list and be roasted accordingly. >
