A responsive voting system

To say that a democratic system of government ought to be responsive to the opinions of the citizens sounds like a truism which could hardly be expected to generate much controversy. Yet, the notion of responsiveness turns out to be open to several nonequivalent interpretations: Condorcet-consistency, monotonicity, invulnerability to the no-show paradox, to name the most important ones. Several results have been achieved to establish incompatibilities between these properties. We shall review some of these and discuss some similar notions and their relationships with those just mentioned. Copyright Springer-Verlag Berlin/Heidelberg 2004