Turnout and quorum in referenda

We analyse the effect of turnout requirement in referenda in the context of a group turnout model. We show that a participation quorum requirement may reduce the turnout so severely that it generates a "quorum paradox": in equilibrium, the expected turnout exceds the participation quorum only if this requirement is not imposed. Moreover, a participation quorum does not necessarily imply a bias for the status quo. We also show that in order to induce a given expected turnout, the quorum should be set at a level that is lower than half tha target, and the effect of a participation quorum on welfare is ambiguous. On the one hand, the quorum decreases voters' welfare by misrepresenting the will of the majority. On the other hand, it might also reduce the total cost of voting. Finally, we show that an approval quorum is essentially equivalent to a participation quorum.