Logrolling affects the relative performance of majority and unanimity rule

We consider a committee facing binary decisions on a number of proposals. If members vote sincerely and payoffs are symmetrically distributed, we show analytically that simple majority rule is the best q-majority rule in an aggregate or expected payoff sense. We argue that this (well known) pattern changes systematically if the committee faces multiple decisions and members engage in logrolling deals. In a simulation exercise, we find that unanimity rule outperforms majority rule when the number of proposals considered is large enough. We complement our analysis with a laboratory experiment designed to investigate whether human subjects engage in the logrolling deals assumed in our simulations. We find that deals associated with large negative externalities are less likely to arise than others, as are "complex" deals involving many voters or proposals. These results suggest that the impact of logrolling on the relative performance of the decision rules considered may be mitigated by cognitive constraints and other-regarding preferences.