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On the terminology of economic design: a critical assessment and some proposals

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Abstract

The purpose of this paper is to provide a critical examination of some of the terminology that is common in economic design and to suggest ways in which it can be improved.

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Notes

  1. It is also confusing to refer to an object allocation problem in which there is only one copy of each object as a school choice problem.

  2. It is important to realize that the benefit comes from the fact that it is the same good that plays that special role for all agents. Having good 1 as the special good for agent and good 2 as the special good for agent 2 would not help. This is why it is preferable to speak of quasi-linear economies, not of quasi-linear preferences.

  3. The fact that the allocation obtained by applying Gale’s algorithm can also be obtained as an equilibrium of something that looks like a market is a mathematical coincidence that has no bearing to the issue at hand, especially because the price-taking behavior would hardly be justified given the unique character of each of the objects owned by the various agents.

  4. The fact that the rule that is arguably most central to handle object-reallocation problem, the so-called top-trading-cycle rule, can be given a market interpretation is irrelevant. There is no reason why a class of problems should be named after a rule that is particular relevance to it.

  5. In “Consistency in generalized economies” (Thomson 1992, 2012), I used the expression “generalized economies” to refer to what I am here proposing to call “mixed-ownership economies”. The term “generalized” is not enough, as it provides no clue as to the type of generalization that is involved.

  6. This is the earliest reference that I could find.

  7. Admittedly, the term “rule” has other meanings. For instance, in the description of an algorithm, it can legitimately be used to designate what is to be done in each of several possible cases that are enumerated. This usage is also common in implementation theory; different cases are distinguished in describing strategy profiles and in each case, a “rule” is applied to determine the outcome.

  8. We noted earlier than the research program associated with Hurwicz’s name has to do with more than the identification of processes that lead to good outcomes, but also with the identification of desirable mappings from economic environments to outcome spaces. However a primary concern of Hurwicz’s as well as of the writers in the so-called socialist controversy indeed was processes. This concern was reflected in the focus of that literature on planning procedures.

  9. By this expression, I mean the problem of either ranking the alternatives in a set or selecting one of them as a function of the list of the preferences of a group of agents, this set not being endowed with any particular structure.

  10. I have had a number of conversations about the school choice problem and a very frequent response when the Boston mechanism was brought up has been “I have attended many presentations where it was discussed but I don’t remember the definition”. All of these conversations were with people who would state the definition of the deferred acceptance rule with no hesitation and I have no doubt that any of them would immediately guess what the expression immediate acceptance could refer to, or at least would easily remember it if presented with the definition.

  11. By definition, the last stage is defined to be the one at which all students are accepted.

  12. It does happen and the possibility underlies the proofs of some characterizations. For example, it is an important step in Schummer’s (1997, 1999) characterizations of the strategy-proof selections from the efficiency correspondence on domains of private good economies (or domains of public good economies) with strictly monotonic and linear preferences. (Indeed, a monotonic transformation at an efficient point is a monotonic transformation at each other efficient point.)

  13. Perhaps we could distinguish between “local” invariance, and “global” invariance. For the property under discussion here, we could say that a rule is “locally invariant” if the following holds: at each point that it selects for a profile, if preferences are subjected to monotonic transformations at this point, then the point is still selected for the new profile. By contrast, a rule would satisfy a “global invariance” property if the entire set of allocations selected for a profile would still be chosen after preferences have been subjected to some transformation: the transformation would be defined in relation to that entire set.

  14. In the context of classical demand theory, the expression “the law of demand” does not seem well justified either since preference relations that violate it are certainly not thought to be pathological.

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  1. University of Rochester, Rochester, NY, USA

    William Thomson

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  1. William Thomson
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Correspondence to William Thomson.

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Thanks to Battal Doğan, Eun Jeong Heo, Alexander Nichifor, Szilvia Pápai, and Utku Ünver for their comments.

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Thomson, W. On the terminology of economic design: a critical assessment and some proposals. Rev Econ Design 22, 67–99 (2018). https://doi.org/10.1007/s10058-018-0210-7

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