Browsing by Author "Thomson, William"

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Cost Allocation and Airport Problems
(2007) Thomson, William
"We consider the problem of dividing the cost of a facility when agents can be ordered in terms of the need they have for it, and accommodating an agent with a certain need allows accommodating all agents with lower needs at no extra cost. This problem is known as the 'airport problem,' the facility being the runway. We review the literature devoted to its study, and formulate a number of open questions."
Fair Allocation Rules
(2007) Thomson, William
From Introduction: "Economists are often criticized for paying little attention to issues of fairness in distribution. It is indeed true that many shy away from making recommendations on the fair allocation of goods and services, perhaps fearing the necessary reliance on value judgments of such recommendations. However, in the last thirty years, a variety of formal criteria of economic justice have been introduced that have broad conceptual appeal as well as significant operational power. Our purpose is to review this literature. Mathematically, the objects of study are mappings that associate with each economy in some domain a non-empty subset of its set of feasible allocations. These mappings are called 'solutions' or 'rules.'"
Lorenz Rankings of Rules for the Adjudication of Conflicting Claims
(2007) Thomson, William
"For the problem of adjudicating conflicting claims, we offer simple criteria to compare rules on the basis of the Lorenz order. These criteria pertain to three families of rules. The first family contains the constrained equal awards, constrained equal losses, Talmud, and minimal overlap rules (Thomson, 2007a). The second family, which also contains the constrained equal awards and constrained equal losses rules, is obtained from the first one by exchanging, for each problem, how well agents with relatively larger claims are treated as compared to agents with relatively smaller claims. The third family consists of consistent rules (Young, 1987). We also address the issue whether certain operators on the space of rules preserve the Lorenz order."
On Properties of Division Rules Lifted by Bilateral Consistency
(2007) Hokari, Toru; Thomson, William
"We consider the problem of adjudicating conflicting claims in the context of a variable population. A property of rules is 'lifted' if whenever a rule satisfies it in the two-claimant case, and the rule is bilaterally consistent, it satisfies it for any number of claimants. We identify a number of properties that are lifted, such as equal treatment of equals, resource monotonicity, composition down and composition up, and show that continuity, anonymity and self-duality are not lifted. However, each of these three properties is lifted if the rule is resource monotonic."
Two Families of Rules for the Adjudication of Conflicting Claims
(2007) Thomson, William
"We define two families of rules to adjudicate conflicting claims. The first family contains the constrained equal awards, constrained equal losses, Talmud, and minimal overlap rules. The second family, which also contains the constrained equal awards and constrained equal losses rules, is obtained from the first one by exchanging, for each problem, how well agents with relatively larger claims are treated as compared to agents with relatively smaller claims. In each case, we identify the subfamily of consistent rules."