An algorithm for finite conjoint additivity

A complete solution to the problem of finite conjoint additivity is provided, not only to answer the question of whether a particular order is conjointly additive, but also to detail the possible value assignments which demonstrate conjoint additivity for the order. In the process, a complete solution is given to the problem of solving a finite number of homogeneous linear inequalities in a finite number of variables. While others have reduced the problem to the solution of systems of linear inequalities, the algorithm presented here is based on “basic inequalities,” and it provides considerable computational simplicity over previous algorithms.