Buying elections for peanuts

We study an election under the influence of an interest group, assuming that a committee must decide between two options—to implement a reform or to stay with the status quo—and that all its members are aligned and in favor of the reform. The decision is taken via simultaneous voting and simple majority. An interest group that prefers the status quo offers an equal share of a “small” budget to any member that votes for against the reform. We demonstrate that even if the available budget is a miniscule fragment of the one required to buy the election for sure (see, e.g., Dal Bò in Am J Polit Sci 51(4):789–803,2007), the interest group can be quite disruptive: there is always a completely mixed equilibrium in which the status quo is the most likely outcome, and the probability of its implementation converges to one as the size of the committee increases. The strategic uncertainty generated by the fact that other equilibria also exist, in which the reform is the most likely winner, seems to be the price that the interest group pays when attempting to buy an election for peanuts. We study the model under different assumptions on how the voting stage proceeds, but concerns on democratic quality do not vanish.