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.
Read more about this topic: Smith Set
Famous quotes containing the words alternative and/or formulation:
“Education must, then, be not only a transmission of culture but also a provider of alternative views of the world and a strengthener of the will to explore them.”
—Jerome S. Bruner (20th century)
“In necessary things, unity; in disputed things, liberty; in all things, charity.”
—Variously Ascribed.
The formulation was used as a motto by the English Nonconformist clergyman Richard Baxter (1615-1691)