Three Axiom Systems for Additive Semiordered Structures
R. Duncan Luce · SIAM Journal on Applied Mathematics · 1973
Axioms are provided for extensive, probability, and (two-component, additive) conjoint structures which are semiordered, rather than weakly ordered. These are sufficient to construct the usual representation for the natural, induced weak order and a tight, threshold representation for the semiorder itself. The fundamental difficulty is in finding axioms that are simple in the primitive semiorder, rather than simple in its induced weak order; from this point of view, the results are only partially successful.