There may be an advantage to a Condorcet efficient method that doesn't always elect from Smith: it may decrease the incentive to bury, since the purpose of the burial strategy is to get a non-Smith member into the top cycle.
However that may be, we can easily and seamlessly enhance MinMax(AWP) to choose from the uncovered set (hence from Smith) in a way that also satisfies Independence from Non-Smith Alternatives: 1. Let C1 be the MinMax(AWP) winner. Elect C1 if it is uncovered, else ... 2. Let C2 be the MinMax(AWP) winner among the alternatives that cover C1. Elect C2 if it is uncovered, else ... 3. Let C3 be the MinMax(AWP) winner among the alternatives that cover C2. Elect C3 if it is uncovered, else ... etc. Proof of Independence from Non_Smith Alternatives: Let C_i be the first member of the sequence C1, C2, ...,W which is in the Smith set. Then C_(i-1) is not in Smith, so the entire Smith set is a subset S of the alternatives that cover C_(i-1). Since C_i is the MinMax(AWP) winner of S, and no defeat of a Smith candidate comes from outside Smith, C_i is also the MinMax(AWP) winner over Smith. In other words, from C_i onward, the non-Smith alternatives are irrelevant. It also turns out that this enhanced method satisfies Independence from Pareto dominated Alternatives, Clone Independence, and Monotonicity. In practice, W will almost always be found on the first or second step of the enhancement. The method is summable in two matrices M and A, where M(x,y) is the number of ballots on which alternative x is ranked above alternative y, and A(x,y) is the number of ballots on which x is ranked but y is not. First form matrix M' by subtracting the transpose of M from M. Then form A' by replacing each positive entry of M' by the corresponding entry of A, while zeroing out the rest of the entries. The positive entries of A' represent the AWP defeat strengths. The covering relations can be recovered from A' as well. So A' has sufficient information to carry out the enhancement. Forest ---- Election-Methods mailing list - see http://electorama.com/em for list info