The Incidence of Some Voting Paradoxes Under Domain Restrictions

Voting paradoxes have played an important role in the theory of voting. They typically say very little about the circumstances in which they are particularly likely or unlikely to occur. They are basically existence findings. In this article we study some well known voting paradoxes under the assumption that the underlying profiles are drawn from the Condorcet domain, i.e. a set of preference profiles where a Condorcet winner exists. The motivation for this restriction is the often stated assumption that profiles with a Condorcet winner are more likely than those without it. We further restrict the profiles by assuming that the starting point of our analysis is that the Condorcet winner coincides with the choice of the voting rule under scrutiny. The reason for making this additional restriction is that—intuitively—the outcomes that coincide with the Condorcet winner make those outcomes stable and, thus, presumably less vulnerable to various voting paradoxes. It will be seen that this is, indeed, the case for some voting rules and some voting paradoxes, but not for all of them.

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

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.