Social and Behavioral Sciences Commons^™

On The Decomposability Of Fractional Allocations, Shurojit Chatterji, Peng Liu

SMU Economics and Statistics Working Paper Series

A common practice in dealing with the allocation of indivisible objects is to treat them as infinitely divisible and specify a fractional allocation, which is then implemented as a lottery on integer allocations that are feasible. The question we study is whether an arbitrary fractional allocation can be decomposed as a lottery on an arbitrary set of feasible integer allocations. The main result is a characterization of decomposable fractional allocations, that is obtained by transforming the decomposability problem into a maximum flow problem. We also provide a separate necessary condition for decomposability.

On The Decomposability Of Fractional Allocations, Shurojit Chatterji, Peng Liu

Research Collection School Of Economics

A common practice in dealing with the allocation of indivisible objects is to treat them as infinitely divisible and specify a fractional allocation, which is then implemented as a lottery on integer allocations that are feasible. The question we study is whether an arbitrary fractional allocation can be decomposed as a lottery on an arbitrary set of feasible integer allocations. The main result is a characterization of decomposable fractional allocations, that is obtained by transforming the decomposability problem into a maximum flow problem. We also provide a separate necessary condition for decomposability.

An Optimal Fair Job Assignment Problem, Zaifu Yang

Cowles Foundation Discussion Papers

We study the problem of how to allocate a set of indivisible objects like jobs or houses and an amount of money among a group of people as fairly and as efficiently as possible. A particular constraint for such an allocation is that every person should be assigned with the same number of objects in his or her bundle. The preferences of people depend on the bundle of objects and the quantity of money they take. We propose a solution to this problem, called a perfectly fair allocation. It is shown that every perfectly fair allocation is efficient and envy-free, …

On Fair Allocations And Indivisibilities, Ning Sun, Zaifu Yang

Cowles Foundation Discussion Papers

This paper studies the problem of how to distribute a set of indivisible objects with an amount M of money among a number of agents in a fair way. We allow any number of agents and objects. Objects can be desirable or undesirable and the amount of money can be negative as well. In case M is negative, it can be regarded as costs to be shared by the agents. The objects with the money will be completely distributed among the agents in a way that each agent gets a bundle with at most one object if there are more …

Feeling The Heat Of Human Rights Branding: Bringing Transnational Corporations Within The International Human Rights Fence, Robert Mccorquodale

Human Rights & Human Welfare

A review of:

Human Rights Standards and the Responsibility of Transnational Corporations edited by Michael K. Addo. The Hague: Kluwer Law International, 1999. 384pp.

A Practical Competitive Market Model For Indivisible Commodities, Zaifu Yang

Cowles Foundation Discussion Papers

A general and practical competitive market model for trading indivisible goods is introduced. There are a group of buyers and a group of sellers, and several indivisible goods. Each buyer is initially endowed with a sufficient amount of money and each seller is endowed with several units of each indivisible good. Each buyer has reservation values over bundles of indivisible goods above which he will not buy and each seller has reservation values over bundles of his own indivisible goods below which he will not sell. Buyers and sellers’ preferences depend on the bundle of indivisible goods and the quantity …

Perfectly Fair Allocations With Indivisibilities, Ning Sun, Zaifu Yang

Cowles Foundation Discussion Papers

One set of n objects of type I, another set of n objects of type II, and an amount M of money is to be completely allocated among n agents in such a way that each agent gets one object of each type with some amount of money. We propose a new solution concept to this problem called a perfectly fair allocation. It is a refinement of the concept of fair allocation. An appealing and interesting property of this concept is that every perfectly fair allocation is Pareto optimal. It is also shown that a perfectly fair allocation is envy …

The Indivisibility Of Economic And Political Rights, Linda M. Keller

Human Rights & Human Welfare

A review of:

Development as Freedom by Amartya Sen. New York: Knopf , 1999 (Paperback Edition: Random House, 2000). 366pp.