This paper develops a political economy model that provides an explanation as for why ruling elites in oligarchic societies may rely on income redistribution to the poor (the masses) in order to prevent them from attempting a revolution. We refer to this kind of redistribution as populist redistribution because, first it does not increase the poor's productive capacity (human capital), and second it seeks to "buy" political support (peace) to perpetuate the elite's control of political power. We examine the conditions under which ruling elites choose to deter the poor (by means of military repression and/or populist redistribution), to engage in a dispute with the poor for the control of political power, or, alternatively, to extend democracy. According to the results of the model populist redistribution (or military repression), if any, increases with initial wealth inequality and with the amount of redistribution that the poor can undertake under democracy, and decreases with the relative importance of a human capital externality in production. The model explains why in some cases the use of an apparently inefficient policy of populist redistribution turns out to be optimal for both groups (the ruling elite and the poor class) when the alternative is the use of military repression or default to conflict.