Toyotaka Sakai

Equitable Intergenerational Preferences on Restricted Domains

This paper examines the existence of equitable preferences on intergenerational consumption paths in an infinite horizon setting. There are two ethical considerations that capture the concept of intergenerational equity: inequality aversion in allocations and equality in treating generations. They are embodied in the Pigou–Dalton principle and anonymity, respectively. We investigate the existence of binary relations that satisfy these two axioms, as well as other standard axioms, such as monotonicity, transitivity, or continuity, on various domains. We show that any domain admitting such a binary relation is quite restricted: its interior is empty and contains no sustainable consumption path.

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 horizons to an infinite time horizon. The future agreement extension of the given orderings is quasi-transitive, complete, and pairwisely continuous. Furthermore, its asymmetric part is larger than that 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.

The manipulability of fair solutions in assignment of an indivisible object with monetary transfers

Public decision making often involves the problem of fairly assigning one indivisible object to agents with monetary transfers. An example is the choice of the location of a garbage incineration facility where the accepting district should receive fair compensations from other districts. In this problem, we show that for broad classes of solutions satisfying a welfare lower bound and an efficiency-oriented condition, the set of equilibrium allocations in the manipulation game associated with a given solution coincides with the set of all envy-free allocations. This generalizes Tadenuma and Thomsons equivalence result for a class of envy-free solutions. Our result covers the Shapley value, which is not covered by Tadenuma and Thomsons result.

Preference Manipulations Lead to the Uniform Rule

In the division problem with single-peaked preferences, it is well known that the uniform rule is robust to strategic manipulation. Furthermore, under efficiency and symmetry, it is the unique strategy-proof rule (Sprumont, 1991; Ching, 1994). We conversely analyze the consequences of strategic manipulation for a wide class of rules. Given a rule, we interpret its associated direct revelation game as a manipulation game, and we characterize its equilibrium allocations. We establish a strong connection between outcomes of manipulation and the uniform rule itself. For every rule that belongs to the class, the uniform allocation (i) is the unique strong Nash equilibrium allocation and the unique Pareto-efficient Nash equilibrium allocation, and (ii) is the unique Nash equilibrium allocation under an additional strict monotonicity condition. Thus, attempts to manipulate each of our rule lead to the recommendation made by the uniform rule. A by-product of our results is the identification of a large class of direct revelation mechanisms that doubly implement the uniform rule in Nash and strong Nash equilibria.

Strategic manipulations of multi-valued solutions in economies with indivisibilities

This paper studies strategic manipulations of multi-valued solutions in the problem of fairly allocating homogeneous indivisible objects with monetary transfers. We provide various extensions of strategy-proofness to multi-valued solutions and examine their impact on standard solutions. We show that some efficient and fair solutions, such as the envy-free solution, satisfy certain extensions of strategy-proofness. We also establish an impossibility result on extended strategy-proofness that is defined in terms of expected utility.

Dichotomous preferences and the possibility of Arrovian social choice

Consider an individual whose judgments are always based on a fundamental criterion such as a political ideology or a religious doctrine. In a choice situation, he always prefers any alternative that is compatible with the criterion to any that is not. When individuals are allowed to have preference spaces restricted in this manner, we investigate Arrow-consistent domains. We observe that a diversity of attitudes is essential in order to escape an Arrovian impossibility.

Nash implementation of competitive equilibria in the job-matching market

This paper studies Nash implementation in the job-matching market where each worker works for only one firm and a firm hires as many workers as it wishes. We show that the competitive equilibrium correspondence (CEC) is the smallest Nash implementable correspondence satisfying individual rationality and Pareto indifference. Furthermore, the CEC is the minimal monotonic extension of the worker-optimal and firm-optimal subcorrespondences. We offer two “good” mechanisms that implement this correspondence in Nash equilibrium.

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.

Considering Collective Choice: The Route 328 Problem in Kodaira City

Abstract A local referendum was held in Kodaira City, Tokyo on 26 May 2013, but the voting box remained sealed. This was because the voter turnout did not reach the 50% threshold for opening the box. Based on the Rousseauian view on voting, we argue that this hurdle is unjustifiable and further question the adequacy of the local referendum even without such a hurdle. Finally, we examine the use of economic mechanisms for this type of collective choice instead of voting.

Limit representations of intergenerational equity

Equal treatment of all generations is a fundamental ethical principle in intertemporal welfare economics. This principle is expressed in anonymity axioms of orderings on the set of infinite utility streams. We first show that an ordering satisfies finite anonymity, uniform Pareto, weak non-substitution, and sup continuity if and only if it is represented by an increasing, continuous function that is a natural extension of the limit function. We then show that whenever such an ordering is infinitely anonymous, it depends only on the liminf and limsup of any utility stream. Our results imply that in ethically ranking utility streams, reflecting only infinitely long-run movements is possible, with liminf and limsup particularly essential, but it is impossible to respect finite generations.