Additive Utility Without Restricted Solvability on All Components

Christophe Gonzales (1)

1 SYSDEF - Systèmes d'aide à la décision et à la formation

Standard theories of additive utility require solvability with respect to all components, which rules out applications where some of the variables are discrete. Possible relaxations of solvability are investigated, in 3-component spaces for the case of restricted solvability, and in n-component spaces for the case of unrestricted solvability. An example is given showing that the Thomsen condition—necessary for the existence of an additive representation—is not implied by the independence axiom when there are only 2 solvable components.

Domaines: Informatique [cs]

Christophe Gonzales. Additive Utility Without Restricted Solvability on All Components. Constructing Scalar-Valued Objective Functions, 453, Springer, pp.64-90, 1997, Lecture Notes in Economics and Mathematical Systems, ⟨10.1007/978-3-642-48773-6_6⟩. ⟨hal-01649126⟩