Median voter theorem has been used in many economic environments including law enforcement. Assumptions of the median voter theorem, however, are generally violated in lawenforcement models. Moreover, it is impossible to have agents with "opposite equilibrium preferences" over enforcement levels...

We prove a general possibility result for collective decision problems where individual allocations are one-dimensional, preferences are single-peaked (strictly convex), and feasible allocation profiles cover a closed convex set. Special cases include the celebrated median voter theorem (Black...