Derivation of the Maximin principleThe Maximin principle classifies States according to the utility of the worst-off actor. The national security function is therefore . The ranking remains unchanged when the same monotonically increasing transformation is applied to each actor utility. In other words, it is invariant under a transformation for which each time . This means that the maximin principle requires level comparability, because the monotonicity of implies that if and only if. To derive the maximin principle, an additional property is necessary: ​​separability, which states that actors for whom all states are alike play no role in the balance of power. More precisely, let there be a subset of actors such that for any tuple of utility functions, it is the same for each state. Then give the same ranking for all actors who are not present, for all states. The idea is that given the comparability of levels and the axioms above, the national security function must be the maximum function. Curiously, however, these premises only imply that the welfare function is maximin or maximax (21). The latter maximizes the utility of the best-off actor; It is, . To deduce a minimax principle, one must exclude the maximax principle for another reason. Again, the idea of ​​the argument can be conveyed in the two-actor case (22), where separability plays no role. Let, as shown in Figure 2, be an arbitrary utility vector, and let . Divide the plane into regions around the diagonal line as shown. It is then sufficient to demonstrate that one of the following two situations must obtain: all the points of the regions and their reflections (gray area in Figure 3) are preferable (or indifferent) to , and all the other points are worse than , or all the points of the regions and their...... middle of paper ...... meaningful tarian calculation. However, the comparability of units remains if the ranking is invariant only under an appropriate subset of translated scaling, while the proof assumes invariance under any translated scaling. In other words, the proof assumes that the utilities have unitary comparability and nothing more than unitary comparability. This strong hypothesis is already very close to utilitarianism. A Rawlsian, for example, would immediately oppose it because it immediately deprives the comparison of the most disadvantaged actors of meaning. If the utility vectors are in state and in state , the Rawlsian prefers due to the higher utility of the more disadvantaged actor. However, a translated rescaling maps these vectors to and , respectively, in which the Rawlsian preference is reversed. A similar point applies to the derivation of a maximin welfare function from the comparability of levels..