Ends against the middle: Determining public service provision when there are private alternatives

Public provision of a service coexists with private market provision. The quality of public provision is determined by majority vote. Preferences are not single peaked owing to the presence of private alternatives. We identify two cases. In one, majority voting equilibrium always exists and the median-income voter is pivotal. Ln the other, a necessary condition for equilibrium identifies the pivotal voter who must have income below the median. When equilibrium exists, a coalition of middle-income households who consume the public alternative win be opposed by a coalition of rich and poor households, with the rich choosing private consumption.