Smith Set - Alternative Formulation

Alternative Formulation

Any binary relation R on a set A can generate a natural partial order on the R-cycle equivalence classes of set A, so that xRy implies ≥ .

When R is the Beats-or-Ties binary relation on the set of candidates defined by x Beats-or-Ties y if and only if x pair-wise beats or ties y, then the resulting partial order is the beat-or-tie order which is a total order. The Smith set is the maximal element of the beat-or-tie order.