Another limited Approval type tiebreaker is N minus 1. If there is a circular tie, then change the number of ranked votes to unranked votes. The choice having the lowest number of votes in the first N minus 1 places would lose or the plurality choice in last place loses. Redo the head the head math using the ranked votes. Repeat, if necessary. Truncated choices would be in a last place tie. Example a voter votes BE with 5 choices-- B > E > (blank) > (blank) > (A=C=D) The major point is that the first N minus 1 ranked votes have a continuing effect as the tiebreaker. However, such a tiebreaker would seem to have the major strategy problems of simple Plurality. Which unranked majority has the least strategy problems as a circular tiebreaker (especially with 4 or more tied choices)---- Left to right (Bucklin) Halfway left to right or right to left (N/2 or halfway Bucklin) Right to left (Reverse Bucklin) ? The above assumes my standard YES/NO vote on candidates in executive and judicial elections but is not used in p.r. elections. It should be noted that having a choice removed in a circular tie is the same as if the remaining choices are to be elected (e.g. 5 to be elected, 6 choices in a tie). Example (from Re: Condorect sub-cycle rule, Sat, Oct 4, 1997 12:18 PM EDT by Markus Schulze)-- 25 BCDFEA 24 CDFEAB 20 ABFECD 15 EABCDF 8 EBCADF 4 ECADBF 4 ECABDF 100 A:B=67:33 A:C=35:65 A:D=51:49 A:E=20:80 A:F=51:49 B:C=68:32 B:D=72:28 B:E=45:55 B:F=76:24 C:D=100:0 C:E=49:51 C:F=80:20 D:E=49:51 D:F=80:20 E:F=31:69 A>B>C>D>F>E>A First 5 choices A 75 B 76 C 100 D 80 E 100 F 69 loses (F is the plurality in last place) 500 A:B=67:33 A:C=35:65 A:D=51:49 A:E=20:80 B:C=68:32 B:D=72:28 B:E=45:55 C:D=100:0 C:E=49:51 D:E=49:51 D is a Condorcet loser. A:B=67:33 A:C=35:65 A:E=20:80 B:C=68:32 B:E=45:55 C:E=49:51 E is the Condorcet winner. If Reverse Bucklin is used however, then-- Unranked votes Last 2 Last 3 A 49 57 B 28 32 C 20 15 D 47 51 E 25 69 F 31 56 200 300 No majority against in last 2 places. E has highest majority against in last 3 places.
