Strategy-proof mechanism design with non-quasi-linear preferences: ex-post revenue maximization for an arbitrary number of objects

We consider the multi-object allocation problem with monetary transfers where each agent obtains at most one object (unit-demand). We focus on allocation mechanisms satisfying individual rationality, non-wastefulness, equal treatment of equals, and strategy-proofness. Extending the result of Kazumura et al. (J Econ Theory 188:105036, 2020b), we show that for an arbitrary number of agents and objects, the minimum price Walrasian is the unique ex-post revenue maximizing mechanism among the mechanisms satisfying no subsidy in addition to the four properties, and that no subsidy in this result can be replaced by no bankruptcy on the positive income effect domain.

Multi-Type Resource Allocation with Partial Preferences

We propose multi-type probabilistic serial (MPS) and multi-type random priority (MRP) as extensions of the well-known PS and RP mechanisms to the multi-type resource allocation problems (MTRAs) with partial preferences. In our setting, there are multiple types of divisible items, and a group of agents who have partial order preferences over bundles consisting of one item of each type. We show that for the unrestricted domain of partial order preferences, no mechanism satisfies both sd-efficiency and sd-envy-freeness. Notwithstanding this impossibility result, our main message is positive: When agents' preferences are represented by acyclic CP-nets, MPS satisfies sd-efficiency, sd-envy-freeness, ordinal fairness, and upper invariance, while MRP satisfies ex-post-efficiency, sd-strategyproofness, and upper invariance, recovering the properties of PS and RP. Besides, we propose a hybrid mechanism, multi-type general dictatorship (MGD), combining the ideas of MPS and MRP, which satisfies sd-efficiency, equal treatment of equals and decomposability under the unrestricted domain of partial order preferences.

Mechanisms for Fair Allocation Problems: No-Punishment Payment Rules in Verifiable Settings

Mechanism design is considered in the context of fair allocations of indivisible goods with monetary compensation, by focusing on problems where agents' declarations on allocated goods can be verified before payments are performed. A setting is considered where verification might be subject to errors, so that payments have to be awarded under the presumption of innocence, as incorrect declared values do not necessarily mean manipulation attempts by the agents. Within this setting, a mechanism is designed that is shown to be truthful, efficient, and budget-balanced. Moreover, agents' utilities are fairly determined by the Shapley value of suitable coalitional games, and enjoy highly desirable properties such as equal treatment of equals, envy-freeness, and a stronger one called individual-optimality. In particular, the latter property guarantees that, for every agent, her/his utility is the maximum possible one over any alternative optimal allocation. The computational complexity of the proposed mechanism is also studied. It turns out that it is #P-complete so that, to deal with applications with many agents involved, two polynomial-time randomized variants are also proposed: one that is still truthful and efficient, and which is approximately budget-balanced with high probability, and another one that is truthful in expectation, while still budget-balanced and efficient.

Special Education: Justice, Tolerance, and Beneficence as Duty1

This article establishes the moral basis for special education as it concerns the duties of justice, toleration, and beneficence. The same fundamental moral principles apply to children with disabilities as to others, but the context here is public education with particular interest in the educational achievement of each child. Special education relies on justice, toleration and beneficence as it seeks the equal treatment of equals. The moral motives for special education are in the liberal democratic ideals of self-determination of every citizen and justice for all. Rights of liberty and justice can be secured, at least imperfectly, by law and regulation. But a civil and humane society needs more than law, more than justice, and more than toleration. It depends also on other civic virtues including respect for and commitment to beneficence.