Benefit-of-the-doubt aggregation and the diet problem

In this note we show that the diet problem and the benefit-of-the-doubt (BoD) aggregation are linear programming duals. That is, the primal (dual) formulation of the diet problem is equivalent to the dual (primal) formulation of the BoD model as long as food prices are set equal to one. In addition, we show that the diet problem and the inverted BoD model are linear programming equivalent as long as the nutritional requirements are set equal to one.