Supplement-- More elementary thoughts about 1 of 2, 2 of 3, 3 of 4, etc. Going beyond the obvious 1 of 2 choices case, there is the N minus 1 choices case when all N choices have majority acceptability (noting that in many elections, 1 or more of the N choices may be unacceptable to many voters). If each voter has N minus 1 YES votes for his/her choices in a tie (2 of 3, 3 of 4, 4 of 5, etc), then 1 of the N choices will have the lowest number of YES votes (assuming no ties) and should lose if there is a circular tie AFTER doing the head to head math. Once again for the umpteenth time, number votes do NOT indicate acceptability but ONLY relative support. A voter's vote might be-- A NO 7 B YES 3 C YES 4 D NO 6 E YES 1 F NO 5 G YES 2 For all voters 1 or more of the choices might get YES majorities. If 3 or more choices get YES majorities, then there is the ever present lurking possibility that 3 or more choices will be in a circular tie using the number votes. With 4 or more choices in a circular tie, the YES votes might be very spread out among such choices. Thus, I suggest that in a tie case that the YES votes in the Nth place on each ballot should be dropped (in ALL elections- legislative, executive, judicial, direct issue) and that the head to head math should be rechecked (repeatedly, if necessary) among the remaining choices. Once again I must complain that too much thinking has been given to the 3 choice tied case and not enough thinking to the 4 or more choice tied cases. The above also brings up the idea of contingent YES votes-- that is, there would be a YES vote for a choice only if certain things happen in the voting (related to the withdrawal idea). The obvious problem is that if many voters have contingent YES votes that a feedback crash/ lock loop might result.
