This paper proposes a simple scheme designed to elicit and reward intensity of preferences in referenda: voters faced with a number of binary proposals are given one regular vote for each proposal plus an additional number of bonus votes to cast as desired. Decisions are taken according to the majority of votes cast. In our base case, where there is no systematic difference between proposals' supporters and opponents, there is always a positive number of bonus votes such that ex ante utility is

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... increased by the scheme, relative to simple majority voting. When the distributions of valuations of supporters and opponents differ, the improvement in efficiency is guaranteed if the distributions can be ranked according to first order stochastic dominance. If they are, the existence of welfare gains is independent of the exact number of bonus votes. * The authors are grateful for the financial support of the National Science Foundation (Grants SES-0084368 and SES-00214013). Alessandra Casella thanks the Institute for Advanced Study in Princeton for its support and hospitality. The paper has bene improved by comments at numerous seminars and conferences and owes an unusually large debt to Russell