Milton, Please excuse me, but as I see it (YMMV) your math is wrong. I'm afraid my example is somewhat complicated, because I pulled the numbers from the thin air and feel sometimes crippled without a blackboard :) [BTW: your guess of the minimal set is pretty close, but see section B below for a smaller set of voters) ::A:: The election rules say that each voter may cast any number 'n' of votes 0<=n<=3 (the ballot form reads "select at most three"). To further complicate the things, NotA (N) has ambiguous value i.e. one mark in the N box may count as 1, 2 or 3 votes. Therefore, there are 15 possible combinations for ticking the four boxes. ABC ABN ACN BCN AB AC BC AN BN CN A B C N 0 (no box is ticked) The number of Ns counts as a threshold against any candidate. And the problem stems from here! ABN means an 'explicit' rejection of C, AN means an explicit rejection of B and C, while AB and A don't mean explicit rejections. Please notice also a somewhat contradictory effect: a voter considers A the optimal choice, and B, C not fit for the position. Then s/he votes AN... but that vote will rise A's threshold. :B: By "the most consensual" I tried to mean the candidate with the largest nonnegative opinions ('for'+'neutral'). In the following example, C has the lowest number of explicit rejections (all non-listed combinations have zero votes): ACN 104 BCN 104 AB 20 A 111 B 97 N 2 Tally: 436 voters. Threshold: 104+104+2 = 210 A: 235 > 220 → pass (with 106 explicit rejections) B: 221 > 210 → pass (with 106 explicit rejections) C: 208 < 210 → fail (with 2 explicit rejections) :C: As a conclusion: this curious voting method may take us out of the impasse now, but has a lot of undersirable properties: is prone to tactical voting, has no monotonicity, does not satisfy the Condorcet ciriterion, etc. Once we get through the current election process, discussing an acceptable voting system seems to be a wise move. Regards from the Far South, Enrique