I show that in a multidimensional spatial model, if an agent is risk neutral on each side of the policy space away from his/her ideal point, then his/her utility function is linearly decreasing not in the Euclidean, but rather in the city block distance to the ideal policy of the agent.

Many economics problems are maximization or minimization problems, and can be formalized as problems of solving “linear difference systems” of the form <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$r_i-r_j \geqq c_{ij}$</EquationSource> </InlineEquation> and r <Subscript> k </Subscript>-r <Subscript> l </Subscript> c <Subscript> kl </Subscript>, for r-unknowns, with given c-constants. They typically involve strict as well as weak...</subscript></subscript></subscript></equationsource></inlineequation>