| Sumario: | The writer examines the implications of the “replacement principle” for the fair allocation of an infinitely divisible commodity among agents with single-peaked preferences. He notes that the principle states that when one of the components of the data entering the description of the problem to be solved alters, all of the relevant agents should be influenced in the same direction—they all gain or they all lose. He applies the principle to situations in which the preferences of one of the agents may alter, in the name “welfare-domination under preference-replacement.” He demonstrates that there is no selection from the no-envy and Pareto solution satisfying it. He weakens the principle by confining its application to situations in which the change is not so disruptive that it turns the economy from one in which there is “too little” of the commodity to one in which there is “too much,” or vice versa. He reveals that the only selection from the no-envy and Pareto solution satisfying this property and “replication-invariance” is the “uniform rule.”
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