Representation in majority tournaments

The paper presents a general setting for studying majority-based collective decision procedures where the electorate is divided into constituencies ac cording to an equal-representation principle. It generalizes the well-known Referendum Paradox to the non-dichotomous choice case, and shows that all Condorcet choice rules are sensitive to the design of the apportionment of the electorate, in the sense that final outcomes may entirely differ from t hose prevailing when there is a single constituency. Direct and representat ive democratic systems thus lead to mutually inconsistent collective decisi ons. (C) 2000 Elsevier Science B.V. All rights reserved.