It is shown that any completely preordered topological real algebra admits a continuous utility representation which is an algebra-homomorphism (i.e., it is linear and multiplicative). As an application of this result, we provide an algebraic characterization of the projective (dictatorial)...

In order to formalize the act of agreement between two individuals, the concept of consensus functional equation, for a bi-variate map defined on an abstract choice set, is introduced. Then, and in a purely choice-theoretical framework, we relate the solutions of this equation to the notion of a...