The simple general case with 3 candidates is-- N1 ABC N2 ACB N3 BCA N4 BAC N5 CAB N6 CBA where N1 .... N6 are numbers of voters. Condorcet thus does A vs. B or N1 + N2 + N5 vs. N3 + N4 + N6 B vs. C or N1 + N3 + N4 vs. N2 + N5 + N6 C vs. A or N3 + N5 + N6 vs. N1 + N2 + N4 --- Plurality does A N1 + N2 B N3 + N4 C N5 + N6 and says that the highest sum wins. --- Davidson does A N3 + N6 B N2 + N5 C N1 + N4 and says that the highest sum loses the first round elimination. I would suggest that it is equally improper to use only partial votes in Plurality as in Davidson (2 of 6 *selections*). Someone may wish to enlighten the list about other methods which do different things with the N1 ... N6 and with 4 or more candidates where there are N x (N-1) X (N-2) x .... x 2 or N factorial (N!) complete combinations. Note- the N1 ... N6 example can be expanded for truncated votes of N7 A N8 B N9 C assuming that AB is the same as ABC, AC is the same as ACB, etc. (thus making 9 numbers involved for 3 candidates). As Mr. Arrow informs us, choosing the *best* method involves various tradeoffs in the strategies regarding the various N1.... Nmost values. I will maintain that majority rule must be an absolute requirement in any method.
