In a model with finitely many agents who have single-dipped Euclidean preferences on a polytope in the Euclidean plane, a rule assigns to each profile of reported dips a point of the polytope. A point <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$x$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>x</mi> </math> </EquationSource> </InlineEquation> of the polytope is called single-best if there is a point <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$y$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>y</mi> </math> </EquationSource> </InlineEquation> of the...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

We consider the problem of reallocating the total initial endowments of an infinitely divisible commodity among agents with single-peaked preferences. With the uniform reallocation rule we propose a solution which satisfies many appealing properties, describing the effect of population and...