Logrolling affects the relative performance of alternative q-majority rules

We consider a committee facing binary decisions on a number of proposals. If members vote sincerely and payoffs are symmetric in expectation, it can be shown that the simple majority rule is the best q-majority rule in an aggregate or expected payoff sense. We argue that this conclusion 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 also conduct a laboratory experiment to investigate whether human subjects engage in logrolling deals and if so which ones. We find that subjects reach some, but not all, of the deals that the experimental situations admit. Deals associated with 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.