Once again --- on the addition (or subtraction) of alternatives and resulting math complications. N1 A>B N2 B>A N1 or N2 is a majority. Choice C comes along. New possible types of votes (ignoring truncated votes) --- CAB ACB ABC N1 Total CBA BCA BAC N2 Total C may (in head to head pairings -- ignoring ties) --- 1. beat both A and B, or 2. beat A, lose to B, or 3. beat B, lose to A, or 4. lose to both A and B. How often would the election result change from the original result with the addition of the 3rd choice ??? (noting the 1, 2 or 3 possible results) Which of the three choices then becomes the most clone like (since 100 percent clones are not likely in larger elections) ??? If the 3 choices suddenly appear to a stranger (with the 6 types of A,B,C votes) , could such stranger know which 2 of them was in the original pairing ??? (i.e. know which of them to eliminate to reproduce such original pairing) Expand the above to 4 or more choices for additional complexities. I beat the dead political horse some more ---- any election method in real public elections operates on the actual choices and the actual votes cast --- NOT with some mythical election with added or removed choices and/or added or removed votes (unless one is dealing with election law felons -- vote robbers, ballot box stuffers, etc.). Many, if not ALL, of the criteria which complain about *strange* things happening with such mythical additions or removals are quite *irrelevant* (because they miss the elementary point of having possible divided majorities if there are 3 or more choices). In particular for a single winner office, one obvious way to get rid of plurality is to require that the winner get a majority in order to be elected. Obviously if he/she cannot get such majority with first choice votes, then the needed additional votes will have to come from 2nd or lower place votes.
