Bribing voters

We present a model of influence over collective decisions made through voting. We show how an outside party offering incentives to a committee can manipulate the committee's decisions at no cost and induce inefficient outcomes. A key condition is that the outsider be able to reward decisive votes differently. Inefficiency results from voting externalities. We relax all initial assumptions to investigate how to insulate committees. We study different information settings, credibility assumptions, payoff structures (voters caring about the collective decision and about their own votes), and incentive schemes (offers contingent on pivotal votes, individual votes, vote shares, and the collective decision). We analyze when voting should be made secret; we elucidate the role of individual accountability and various political institutions in preventing vote buying. We discuss implications for lobbying, for clientelism, for decisions in legislatures, boards, and central banks, and for the efficiency of democracy.