Below is the 4 choice general circular tie case with each choice grouped last (6 each) (assuming no truncated votes). N number= a number of votes Perhaps it will enlighten as to how to get a majority consensus winner in all cases (3 to M(any) choices in a circular tie). The 3 choice general case with only 6 possible types of votes (assuming no truncated votes) is not complex enough. Assume A>B>C>D>A or some other type of circular tie. Each type of circular tie means that various combinations of the N values are related (such as-- if A > B, then the sum of N7 to N12, N13, N14, N17, N19, N20, N23 is greater than the sum of N1 to N6, N15, N16, N18, N21, N22, N24) (i.e. the sum of 12 values each)). Thus, there is some major complexity if all 24 types of votes are used in examples (which partially helps to explain why the single winner problem has been around since the days of Condorcet and Borda 1770's-1780's). Throw in the various criterion of various folks and the complexity becomes overwhelming. Perhaps someone might post the various criterion that have been thought about. I will only observe that the tiebreaker must deal with how the voters actually vote whether or not they are sincere (noting that polls will be taken before the votes are cast). N1 BCDA N2 BDCA N3 CBDA N4 CDBA N5 DBCA N6 DCBA N7 ACDB N8 ADCB N9 CADB N10 CDAB N11 DACB N12 DCAB N13 ABDC N14 ADBC N15 BADC N16 BDAC N17 DABC N18 DBAC N19 ABCD N20 ACBD N21 BACD N22 BCAD N23 CABD N24 CBAD Anybody want to do the 5 choice general case (120 types of votes with 60 types of votes where each choice beats each other choice) ?
