Duverger's Hypothesis, the Run-Off Rule, and Electoral Competition

I analyze a model of electoral competition with entry under the run-off rule. I find that a continuum of equilibria exist in which one of two dominant parties always win, and that there are no other equilibria. Thus, if parties are victory seeking then only two parties will enter the election. This finding conflicts with the accepted wisdom on the run-off rule encapsulated by "Duverger's Hypothesis." The results of the model are then reconciled with Duverger's Hypothesis and a more precise formulation is proposed.