Democracy undone. Systematic minority advantage in competitive vote markets

We study the competitive equilibrium of a market for votes where the choice is binary and it is known that a majority of the voters supports one of the two alternatives. Voters can trade votes for a numeraire before making a decision via majority rule. We identify a sufficient condition guaranteeing the existence of an ex ante equilibrium. In equilibrium, only the most intense voter on each side demands votes, and each demands enough votes to alone control a majority. The equilibrium strongly resembles an all-pay auction for decision power: it makes clear that votes are only a medium for the allocation of power. The probability of a minority victory is always higher than efficient and converges rapidly to one-half as the electorate increases, for any minority size. The numerical advantage of the majority becomes irrelevant: democracy is undone by the market.