Limitations of the spatial model

One approach to avoiding the implications of Arrow's paradox is to impose restrictions on the preferences of voters. A restriction often assumed in the literature is that voters' preferences can be represented by a choice among points in a space, where voters' preferences are convex. We claim that these assumptions will often be unjustified. Government must often address issues of externalities or public goods, which means that the possibility frontier will not be concave. This in turn means that voters' preferences over feasible policies will not be convex.