We show that any complete, lower-semicontinuous, and translation- invariant preorder defined on a topological vector space admits a linear and continuous utility representation.

The purpose of this addendum is to correct some results published in our paper "Some issues related to the topological aggregation of preferences" (SCW (1992) 9: 213-227). <!--ID="" Acknowledgements. Thanks are given to Prof. Boris A. Efimov and Gleb A. Koshevoy (Moskow, Russia), Luc Lauwers (Leuven, Belgium) and Michael Sunderland (Oxford, U.K.) for their valuable suggestions and comments.-->

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...

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)...

Necessary and sufficient conditions are presented for the existence of a pair u,v of positively homogeneous of degree one real functions representing an interval order [InlineMediaObject not available: see fulltext.] on a real cone K in a topological vector space E (in the sense that, for every...

We analyze the structure of a semiorder, paying attention to its representability through a real-valued function and a positive constant threshold (the so-called Scott-Suppes representation). We furnish a new set of sufficient conditions for the Scott-Suppes representability of semiorders....

In this paper we study an astonishing similarity between the utility representation problem in economics and the entropy representation problem in thermodynamics.

This paper studies the topological approach to social choice theory initiated by G. Chichilnisky (1980), extending it to the case of a continuum of agents. The social choice rules are continuous anonymous maps defined on preference spaces which respect unanimity. We establish that a social...