We introduce the notion of combinatorial vote, where a group of agents (or voters) is supposed to express preferences and come to a common decision concerning a set of non-independent variables to assign. We study two key issues pertaining to combinatorial vote, namely preference representation and the automated choice of an optimal decision. For each of these issues, we briefly review the state of the art, we try to define the main problems to be solved and identify their computational complexity. This paper is a revised and extended version of the paper entitled "From preference representation to combinatorial vote", Proceedings of the Eighth International Conference on Principles of Knowledge Representation and Reasoning (KR2002), pages 277-288, Morgan Kaufmann, 2002. c 2003 Kluwer Academic Publishers. Printed in the Netherlands. amai-lang.tex; 3/07/2003; 12:30; p.1