The replacement principle in economies with single-peaked preferences

Our objective is to investigate the implications of the ''replacement principle'' for the fair allocation of an infinitely divisible commodity among agents with single-peaked preferences, The principle says that when one of the components of the data entering the description of the problem to be solved changes, all of the relevant agents should be affected in the same direction: they all gain or they all lose. We apply it to situations in which the preferences of one of the agents may change, under the name of welfare-domination under preference-replacement. We show that there is no selection from the no-envy and Pareto solution satisfying it. Then, we weaken it by limiting 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 conversely. We show that there is only one selection from the no-envy and Pareto solution satisfying this property and replication-invariance. It is the ''uniform rule,'' a solution that has played a central role in previous analyses of the problem. (C) 1997 Academic Press.