The paper investigates the Pareto efficiency of direct democracy and searches for the frequency with which the losing minority in referendum voting could compensate the majority and still be better off. A model is defined that permits the measuring of the intensity of preferences in a population, based on voting and abstention behavior. Using the model, an analysis of over 100 Swiss referenda reveals only a few instances in which the outcome of direct voting is inefficient. It seems that the political system evolves methods of trade-off that permit efficient outcomes in most cases. Criticism of direct democracy should therefore not rely on the primarily hypothetical objection of inefficiency.