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Mechanism design is concerned with settings where a policy maker (or social planner) faces the problem of aggregating the announced preferences of multiple agents into a collective (or social), system-wide decision. One of the most important ways for ...

We characterize the class of Arrovian Social Welfare Functions (ASWFs) as integer solutions to a collection of linear inequalities. Many of the classical possibility, impossibility, and characterization results can be derived in a simple and unified way ...

The no-free-lunch theorem of optimization (NFLT) is an impossibility theorem telling us that a general-purpose, universal optimization strategy is impossible. The only way one strategy can outperform another is if it is specialized to the structure of ...

We show that certain reasonable axioms for an optimal solution to the problem of locating a facility on a network, i.e., axioms of distance determination, Pareto optimality, and anonymity, and a weak Lipschitz condition, can be self-contradictory. In ...