Are Referendums and Parliamentary Elections Reconcilable? The Implications of Three Voting Paradoxes

Abstract In representative democracies, referendum voting and parliamentary elections provide two fundamentally different methods for determining the majority opinion. We use three mathematical paradoxes – so-called majority voting paradoxes – to show that referendum voting can reverse the outcome of a parliamentary election, even if the same group of voters have expressed the same preferences on the issues considered in the referendums and the parliamentary election. This insight about the systemic contrarieties between referendum voting and parliamentary elections sheds a new light on the debate about the supplementary value of referendums in representative democracies. Using this insight, we will suggest legal conditions for the implementation of referendums in representative democracies that can pre-empt the conflict between the two methods for determining the majority opinion.