Uniform, Equal Division, and Other Envy-free Rules between the Two

This paper studies the problem of fairly allocating an amount of a divisible resource when preferences are single-peaked. We characterize the class of envy-free and peak-only rules and show that the class forms a complete lattice with respect to a dominance relation. We also pin down the subclass of strategy-proof rules and show that the subclass also forms a complete lattice. In both cases, the upper bound is the uniform rule, the lower bound is the equal division rule, and any other rule is between the two.

Intergenerational equity and an explicit construction of welfare criteria

Ranking infinite utility streams includes many impossibility results, most involving certain Pareto, anonymity, or continuity requirements. We introduce the concept of the future agreement extension, a method that explicitly extends orderings on finite time horizon to an infinite time horizon. The future agreement extension of given orderings is quasi-transitive, complete, and pairwisely continuous. Furthermore, it is a subrelation of any other pairwisely continuous extension of the orderings. In case of anonymous and strongly Paretian orderings, their future agreement extension is variable step anonymous and strongly Paretian. Characterizations of the future agreement extensions of the utilitarian and leximin orderings are obtained as applications.Future agreement extension, Variable step anonymity, Intergenerational equity, Infinite generations, Diamond's impossibility theorem

An axiomatic approach to intergenerational equity

We present a set of axioms in order to capture the concept of equity among an infinite number of generations. There are two ethical considerations: one is to treat every generation equally and the other is to respect distributive fairness among generations. We find two opposite results. In Theorem 1, we show that there exists a preference ordering satisfying anonymity, strong distributive fairness semiconvexity, and strong monotonicity. However, in Theorem 2, we show that there exists no binary relation satisfying anonymity, distributive fairness semiconvexity, and sup norm continuity. We also clarify logical relations between these axioms and non-dictatorship axioms.

Nash implementation of competitive equilibria in the job-matching market

Job-matching, Many-to-one matching, Nash implementation, Mechanism design, Monotonic extension, Indivisible goods, C78, D78, J41,