Mr. Layton asked- Incidentally, do you (and I would like to hear responses from other list members as well) support optional preferential or compulsory preferential or something in between (ie a minimum number of preferences be expressed for a vote to be considered valid)? While truncated votes cause significant problems for pairwise comparisons, should a vote where the intention of the voter is clear (ie a single number 1, or a single x) be declared invalid, simply because it causes difficulties? --- D- 1. No minimum. 2. In view of the place votes table, each truncated choice should have 1/N vote in each place involved, as I noted about 2 weeks ago. Example A voter votes CB [A=D=E] A, D and E should get a 1/3 vote each in the 3rd, 4th and 5th places of a place votes table from such ballot (computerized votes needed in large elections). However, in each head to head pairing, there would be a majority of all votes (MOAV) winner (assuming no ties) if each choice involved has a 1/2 vote. Example 45 G > H ranked votes 5 G > [H = other] truncated votes 33 H > G ranked votes 7 H > [G = other] truncated votes 10 Other > [G=H=other] truncated votes 100 G vs H head to head G 45 + 5 + 10/2 = 55 H 33 + 7 + 10/2 = 45 100 = 100
