Crafting consensus

The paper analyzes the problem of a committee chair using favors at her disposal to maximize the likelihood that her proposal gains committee support. The favors increase the probability of a given member approving the chair’s proposal via a smooth voting function. The decision-making protocol is any quota voting rule. The paper characterizes the optimal allocation of any given level of favors and the optimal expenditure-minimizing level of favors. The optimal allocation divides favors uniformly among a coalition of the committee members. At a low level of favors, the coalition comprises all committee members. At a high level, it is the minimum winning coalition. The optimal expenditure level guarantees the chair certain support of the minimum winning coalition if favors are abundant and uncertain support of all committee members if favors are scarce; elitist or egalitarian committees are compatible with a strategic chair. The results are robust to changing the chair’s objectives and to alternative voting functions, and reconcile theoretical predictions with empirical observations about legislative bargaining experiments, lobby vote buying and executive lawmaking.