A note on Thomson's characterizations of the uniform rule. - Dagan, Nir (Journal of Economic Theory, 1996)
A commentary on W. Thomson's “Consistent solutions to the problem of fair division when preferences are single-peaked,” which appeared in the Journal of Economic Theory, vol. 63, 1994, pp. 219-245. Thomson proved that the uniform rule of the problem of the fair division of an infinitely divisible and homogeneous commodity among agents whose preferences are single-peaked is the unique rule that is bilaterally consistent, continuous, Pareto optimal, and envy free in a setting of an infinite number of potential agents. The writer demonstrates, however, that the impact of consistency is greater than implied by Thomson and that the uniqueness of the uniform rule is achieved without assuming continuity, even in a setting of a finite number of potential agents. In addition, the writer states that a similar finding is obtained by replacing envy-freeness with individual rationality from equal division.