Plurality or proportional representation

Normatively it might be desirable to use direct democracy for all social choices. But there are two main difficulties with the principle that all political decisions should be made by calling on the whole electorate to vote by referendum. The first is the gross inefficiency of requiring voting on every decision. The second is the problem of instability. Much theoretical analysis (some reviewed in this volume) suggests that if there is heterogeneity in the electorate, then the generic voting paradox exists. Namely, whatever is proposed can always be beaten by some new majority. The only time this will not occur is when the decision can be described in some way as fundamentally one-dimensional. So for example, if all decisions are defined by left or right, then there can exist an equilibrium or “core” political decision that is characterized by having half the voters on one side and half on the other. If there are two or more dimensions, then typically such an equilibrium or core will not exist. I shall return to this question of instability.

If direct democracy is ruled out, then the alternative is representative democracy. This requires “choice” of an electoral system to determine who shall represent the citizens. One system, namely proportional representation (PR), allocates seats to the various parties in something close to direct proportion with the number of votes garnered by those same parties.