Truncated votes may provide a clue to a head to head circular tie tiebreaker. The very simple case (i.e. Plurality)-- N1 A > blank > (B=C) N2 B > blank > (A=C) N3 C > blank > (A=B) The last place totals- A N2 + N3 B N1 + N3 C N1 + N2 One of such last place totals for a choice will be the highest (assuming no ties). Should such choice lose ? Should expanding upon Plurality change the loser ? N1 A > B > C N2 A > C > B N3 B > A > C N4 B > C > A N5 C > A > B N6 C > B > A Assuming majority acceptability for each choice and a circular tie, then the last 2 place votes are-- A N3 + N4 + N5 + N6 B N1 + N2 + N5 + N6 C N1 + N2 + N3 + N4 One of such 2 last place totals for a choice will be the highest (assuming no ties). Should such choice lose ? The above applies to 4 or more choices. N1 A > blank > blank > ... > (B=C= ... =Y=Z) etc. N26 Z > blank > blank > ... > (A=B= ... =X=Y) Expanded into a circular tie--- N1 A > B > C > ... > Z N2 A > C > B > ... > W etc. N26f Z > Y > X > ... > A (26f= 26 factorial) Note the possibility of clones (i.e. if N1= N2, then B and C are twins) (but very unlikely in a large public election). The sum of the votes in the last P places will produce one or more majorities against. Should such choice(s) or only the highest majority against choice lose successively ? See also the Reverse Bucklin series.
