Abstract
The purpose of this note is to propose a two-way classification of the axioms of the theory of economic design, and to map out directions for future research that we perceive as particularly promising.
I thank Shigehiro Serizawa for useful comments.
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Notes
- 1.
We are not addressing here the role of axioms in other areas of economics, such as decision theory, nor in other fields, such as mathematics. For a discussion of the axiomatic method in some theory and resource allocation, see Thomson (2001).
- 2.
- 3.
Yet, not keeping them in mind may be damaging. For example, the failure to distinguish between punctual and relational axioms has been responsible for an erroneous interpretation of the consistency principle and of some results involving consistency axioms (Thomson 2012).
- 4.
Efficiency is a punctual axiom. Resource monotonicity,  which says that if the resources available to society become more abundant, every agent should end up at least as well off as he was made initially, is a relational axiom.
- 5.
Resource monotonicity (footnote 3) is a pre-application axiom. Consistency, which says that if some agents leave with their assignments, and the situation is reevaluated at this point, each of the remaining agents should be assigned the same thing as initially, is a post-application axiom.
- 6.
The individual endowment lower bound, which says that each agent should find his assignment at least as desirable as his private endowment, is a self-regarding axiom. Other-regarding endowment monotonicity, which says that when an agent’s private endowment increases, each of the others should end up at least as well off as he was made initially, is an other-regarding axiom.
- 7.
Respect of unanimity is another example.
- 8.
Other-regarding endowment monotonicity (footnote 5) is an example.
- 9.
This says that when an agent’s private endowment increases, he should end up at least as well as was made initially.
- 10.
Why did it take so long for a group version of non-bossiness (the requirement that, if an agent’s assignment does not change as a response to a change in his preferences, no one else’s assignment change either), to be formulated?
- 11.
These axioms are related in multiple ways. This should be expected. The richer one’s formulation of axioms for a model, the more likely they will be logically related.
- 12.
Consider a society simultaneously facing two allocation problems; these problems are of the same type and they can be added, for example two cost allocation problems implicating the same agent set, such as a university contracting with the same list of suppliers for two construction projects. Additivity says that they can be handled separately, each agent receiving two bills, one for each of them, or consolidated into one and handled as one problem.
- 13.
This says that no agent should prefer someone else’s assignment to his own.
- 14.
This says that the assignment of no agent should dominate commodity by commodity the assignment of anybody else.
References
Chaudhuri, A. (1986). Some implications of an intensity measure of envy. Social Choice and Welfare, 3, 255–270.
Chun, Y., & Thomson, W. (1989). Bargaining solutions and relative guarantees. Mathematical Social Sciences, 17, 295–295.
Cho, W. (2014). Impossibility results for parametrized notions of efficiency and strategy-proofness in exchange economies. Games and Economic Behavior, 86, 26–39.
Diamantaras, D., & Thomson, W. (1990). An extension and refinement of the no-envy concept. Economics Letters, 33, 217–222.
Harless, P. (2017a). Wary of the worst: maximizing award guarantees when new claimants arrive. Games and Economic Behavior, 105, 316–328.
Harless, P. (2017b). Guarantee structures for claims problems; properties and comparisons among rules. Mimeo.
Hurwicz, L. (1972). On informationally decentralized systems. In C.B. McGuire & R. Radner, (Eds.), Decision and Organisation (pp. 297-336). Minneapolis: University of Minnesota Press.
Lensberg, T., & Thomson, W. (1983). Guarantee structures for problems of fair division. Mathematical Social Sciences, 3, 205–218.
Moulin, H., & Thomson, W. (1988). Can everyone benefit from growth? Two difficulties. Journal of Mathematical Economics, 17, 339–345.
Schummer, J. (2004). Almost-dominant strategy implementation: Exchange economies. Games and Economic Behavior, 30, 154–170.
Tadenuma, K., & Thomson, W. (1995). Refinements of the no-envy solution in economies with indivisible goods. Theory and Decision, 39, 189–206.
Thomson, W. (1983). Collective guarantee structures. Economics Letters, 11, 63–68.
Thomson, W. (1987a). Individual and collective opportunities. International Journal of Game Theory, 16, 245–252.
Thomson, W. (1987b). Can everyone benefit from growth? Another impossibility. University of Rochester, Mimeo.
Thomson, W. (2001). On the axiomatic method and its recent applications to game theory and resource allocation. Social Choice and Welfare, 18, 327–387.
Thomson, W. (2003). Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: A survey. Mathematical Social Sciences, 45, 249–297.
Thomson, W. (2012). On the axiomatics of resource allocation: Interpreting the consistency principle. Economics and Philosophy, 28, 385–421.
Thomson, W. (2016). Non-bossiness. Social Choice and Welfare, 47, 665–696.
Thomson, W. (forthcoming 2019a). How to divide when there isn’t enough: From Aristotle, the Talmud, and Maimonides to the axiomatics of resource allocation. Monograph of the econometric society. Cambridge: Cambridge University Press.
Thomson, W. (2019b). Let’s Talk about Economic Design.
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Thomson, W. (2019). On the Axiomatics of Resource Allocation: Classifying Axioms and Mapping Out Promising Directions. In: Laslier, JF., Moulin, H., Sanver, M., Zwicker, W. (eds) The Future of Economic Design. Studies in Economic Design. Springer, Cham. https://doi.org/10.1007/978-3-030-18050-8_29
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