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)...

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.-->

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....