Majority rules are frequently used to decide whether or not a public good should be provided, but will typically fail to achieve an efficient provision. We provide a worst-case analysis of the majority rule with an optimally chosen majority threshold, assuming that voters have independent...

How should a society choose between two social alternatives if participation in the decision process is voluntary and costly and monetary transfers are not feasible? Considering symmetric voters with private valuations, we show that it is utilitarian-optimal to use a linear voting rule: votes...