The below assumes that each choice gets a YES majority of all of the voters on a YES/NO vote. A simple circular tie in a single winner case -- 35 ABC 34 BCA 31 CAB 100 66 A > 34 B 69 B > 31 C 65 C > 35 A A>B, B>C, C>A If D is made a 100 percent clone of B, then there is 35 ABDC 34 BDCA 31 CABD 100 A > B and D, B and D > C, C > A, 100 B > 0 D Going backwards, even the 2 or 3 choice cases can be deemed to have an element of cloneness. Namely, the largest head to head defeat shows the largest clone (noting that head to head comparisons may involve direct opposites or real clones). With 3 or more choices, eliminating one choice at a time may, of course, cause a bad defeat (by such losing choice) to be removed. Example 27 ABCD 26 BCDA 25 CDAB 23 DABC 101 75 AB 26 50 AC 51 27 AD 74 76 BC 25 53 BD 48 78 CD 23 A > B, B > C, C > D, D > A -- Rearranging-- Highest defeat 78 CD 23 76 BC 25 75 AB 26 74 DA 27 lowest worst defeat 53 BD 48 51 CA 50 Lowest defeat 407 199 Totals 606 Is D the largest clone ? Note the DA line. If D is eliminated, then there is 76 BC 25 75 AB 26 51 CA 50 202 101 Totals 303 If C is eliminated, then A beats B. Would a circular tie winner always be near the median in a vertical arrangement if the highest defeated clones lose ??? Another somewhat obvious tiebreaker would have the highest YES votes choice be the winner (if there is no Condorcet winner). I note again that any tiebreaker must be rather obvious to get adopted into law for real public elections.
