Some remarks on the concept of proportionality

Proportionality plays a role in many principles of fairness or justice. In particular, it is often invoked in electoral systems aiming at a similarity of opinion distributions in the parliament and in the electorate at large. The proportional systems of representation (PR systems, for short) strive for maximal similarity between these two distributions. Unfortunately, the concept of proportionality is imprecise in two senses: it is vague and ambiguous. In other words, once a clear criterion of what we mean by proportionality is given, different PR systems may differ in the degree of proportionality achieved in any given election. This is what will be referred to as the vagueness of proportionality (of election outcomes). Proportionality is, however, also ambiguous in that it refers to different things depending on how the voters are expected to signal their opinions and on what is it that one wishes to distribute proportionally.