Majority voting with single-crossing preferences

We clarify and extend a number of sufficient conditions for the existence of a majority voting equilibrium on one-dimensional choice domains. These conditions, variously stated in the previous literature, all impose order restrictions on voter preferences (for instance, monotone marginal rates of substitution) which we show to imply or be equivalent to a general, ordinal version of the single-crossing condition. This simple property is economically intuitive and easily checked in applications. This ease of application is demonstrated through an examination of voting models of redistributive income taxation and trade union bargaining behaviour.