- 29 May 2008
- Working Paper Summaries
This paper considers allocation and bargaining problems, and introduces conditions that one might expect fair procedures to satisfy. However, not all conditions one might hope for can be satisfied simultaneously. Furthermore, some apparently plausible and widely proposed axioms and procedures have consequences whose undesirability clearly goes far beyond what can be excused in this way. Thus pitfalls lurk in the field of fair division. Key concepts include: The first condition, "nondiscrimination," asserts that, in an allocation problem, if two agents receive probability shares of the same item and no chance of any other, then their shares should be proportional to their entitlements. The remaining, "monotonicity" conditions apply to two agents and assert that a change in the feasible set that increases the utility cost to one agent of providing any given utility gain to the other should not hurt the first agent, or at least the solution should not change. Closed for comment; 0 Comment(s) posted.
- 04 Oct 2007
- Working Paper Summaries
"Fair" could be defined as what people of good will would want to be. This does not constitute an operational definition, however. This paper provides a specific procedure to calculate what could be considered fair and reasonable for various situations that require a fair division. A simple example would be a family that has inherited objects of artistic and/or sentimental value and wants to divide them up fairly while taking into account differences in taste. Laymen, mathematicians, and economists all have their own proposals for creating a fair division. Pratt suggests a procedure that, when put to the test of a range of examples, produces outcomes that accord with our intuitive sense of what is fair and desirable while previously proposed procedures do not. Key concepts include: The procedure measures the value of each object in terms of its desirability to the various participants. It allocates the objects so that the participants receive the same total value (or value proportional to their entitlements if they are unequal), without envy or waste ("money left on the table"). Randomization is used if needed to accomplish this. Many procedures work well on average problems. Indeed, all reasonable procedures are much alike in near-symmetric problems. It is the lopsided examples that test the procedures, especially with more than two participants. Participants are not penalized for receiving objects of no value to anyone else or for being honest about their values for such objects. Closed for comment; 0 Comment(s) posted.