• Bounded Rationality by Ben O’Neill

    No, market-design theory does not show “market failure”
    Ben O’Neill
    University of New South Wales.
    Email: ben.oneill@hotmail.com

    Volume 1, Issue 1, pages 13 – 16

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    The past year has seen some interesting commentary on the Nobel Prize in economics awarded last year to Professors Lloyd Shapley and Alvin Roth who have been major contributors to a branch of economic theory known as “market design”.  This is an interesting branch of economics and gives important insights into the design of transaction systems in markets that are subject to constraints that prevent outside trade and payment.

    Shapley and Roth have undertaken some very insightful and useful work in this field, but it is often presented in a language which is highly misleading.  Indeed, the very term “market design” grates against the Hayekian idea of spontaneous order under the free market and the Misesian view of the calculation problems in central planning.  When coupled with mentions of “market failure”, the term suggests that the allocation process in the market must be consciously designed by some outside agent, rather than emerging spontaneously from the voluntary choices of participants.

    Running with this idea, Ritter and Wiseman (2012) reported on the prize citing a statement from a former student of Professor Roth, who says that Roth “…has spent a lot of time studying markets where things don’t work out.  It’s not like we could just buy and sell kidneys, and people can’t buy their way into public schools.  So standard economic models don’t apply”.

    Cases where “markets don’t work out”

    The example given, on the restriction against buying and selling human kidneys, actually gives a hint as to the real state-of-affairs in this area of economic research, and the so-called “market failure” that is addressed.  Actually, we could just buy and sell human kidneys, if only this wasn’t prohibited by the coercive interference of government.  There is no inherent market problem that prevents this kind of transaction from taking place.  Rather, what has occurred is that this transaction is prohibited by government statutes, and this is done on the basis of an alleged moral repugnancy in selling human organs — a reason having nothing to do with any failure of the free market system.

    Roth (2012) discusses this kind of “repugnancy constraint” on markets, noting that this constraint is imposed by government intervention based on the alleged moral repugnancy of the transaction.  He also notes that this reaction of repugnancy is often based on concerns about “objectification” of something that people do not wish to see bought and sold, or on an alleged “exploitation” of the poor (pp. 44-45).  (Both of these objections derive from Marxist critiques of voluntary trade and monetary transactions.)  Roth also notes that these objections run into some cogent rebuttals from economists (pp. 49-50).  In particular, the latter objection is contrary to the fact that a voluntary transaction of this kind is welfare-enhancing even from the point of view of the poorer person who sells their own kidney for money.

    Roth’s analysis of “repugnancy constraints” discusses the fact that markets are often constrained from operating by government intervention on the basis of the alleged repugnancy of some kind of voluntary transaction.  Actually, he does not assert that markets “don’t work out” in these cases, but that they have been prevented from working in their normal way by prohibition on a particular kind of transaction.

    Shapley and Roth’s work on matching-problems

    Much of the insight into market design in these cases spawned from an early algorithm developed by Professor Shapley and another economist to deal with a particular constrained market problem (Shapley and Gale 1962).  They considered a hypothetical situation where a group of equal numbers of men and women want to pair up to marry one another, and each person has some ranking-order for the how desirable each partner is to them.  The problem here is that some men might prefer the same women and some women might prefer the same men, such that the satisfaction of one removes a desirable partner from the other.  Moreover, the problem is designed in such a way that it does not allow consideration of any outside benefits.  (Perhaps the couples take the view that outside payment would undermine the display of love shown in the coupling.)

    Roth (1982) looks at various properties that are desirable in this pairing allocation and determines whether these desirable properties can be achieved.  He begins by looking at whether a particular pairing arrangement is “unstable” or not.  A pairing arrangement is defined to be unstable if there is a man and a woman who are not paired together, but they would both prefer to be paired with each other than with their present partner.  (This is unstable because presumably they will each leave their present partner to be together).  He shows that regardless of the underlying preferences of the men and women in the matching problem, there will always be at least one stable pairing arrangement available (p. 620, Theorem 1).  This achieves a standard property of the free market system, where stability is ensured by the fact that all voluntary transactions are allowed.

    Roth also looks at another desirable property of a pairing system called “truthful revelation”.  Once the rules of the matching system are set by the market designer, the various men and women will compete to get a desirable partner.  Ideally, we would like for it to be in each person’s strategic best interests to tell the truth about his or her preference ranking for partners under this system.  After all, if there is an incentive for a person to lie, this makes it hard to establish who really wants who, and this loss of information means that the pair matching does not work well.  Again, this is a standard property of the free market system, where the price system signals costs to producers and consumers and they reveal their preferences implicitly through their transactions and abstention from other transactions.

    Roth shows that regardless of the underlying preferences of the men and women in the matching problem, it is always possible to create a matching system that removes any incentives to lie (p. 623, Theorem 4).  In particular, it is possible to create a system which gives the best stable pairing from the point of view of either the men or the women (but not both) and in this case, that group has no incentive to lie about their preferences (pp. 620-621, 623-624, Theorems 2 and 5).

    So the question is, is it possible to have both of these desirable properties together?  In other words, in the context of constrained matching problems, is it possible to create a pairing system that is both stable and removes any incentive to lie for the general case of this matching problem?  The answer, unfortunately, is no (p. 622, Theorem 3).  Roth’s work shows that it is possible to choose a stable pairing that is the best stable pairing for the men, or it is possible to choose a stable pairing that is the best stable pairing for the women, but these will not necessarily coincide.  Moreover, having set this system of market design, it is impossible to remove incentives for the unfortunate group to lie — this may be an optimal strategy for some people in that group.  Unlike the case prevailing in a free market system, these two desirable properties cannot be simultaneously achieved.

    Shapley and Roth’s subsequent work has parlayed this basic idea into the development of algorithms that try to minimise the undesirable aspects of constrained markets.  This has been applied in the constrained market for organ donation (no sales allowed) and the constrained market for university entry (no purchase of entry allowed).  Through “market design” the economists are able to reduce —but not eliminate— the damage done by the imposition of the initial constraint.

    Implications of this work

    Roth and Shapley have often presented their work as a method of dealing with so-called “market failures”, though what they mean when they use this term is curious indeed (see e.g., Roth 2008).  An examination of each of the situations they describe in their work shows that they are actually talking about situations where there is a direct government provision of services under a self-imposed constrained arrangement, or a government intervention into the market which creates the constraint.  Professor Roth explains his particular interest in the problem of “market design” by noting that his attempts to improve the functioning of various markets have tended to run up against repugnancy arguments claiming that certain free-market transactions are inappropriate (ibid, p. 50).  He has therefore developed his theory as a means of coping with these constraints as best as can be done.

    It is extremely wrongheaded for this work to be presented as antithetical to the free-market, with talk of “market failure” and other nonsense.  In fact, the foundational work done in this area by Roth actually proves that this centralised market design cannot replicate basic desirable properties that arise on the free market.  Any “market design” in this area will either be unstable, or will create incentives for market participants to lie about their true preferences in order to get their preferred result.  Each stable arrangement identified by the work in Shapley and Roth will either be suboptimal from the point of view of one group or another, meaning that the designed market lacks the optimal pairing properties that are standard when dealing with an unconstrained free market.

    Even setting aside these problems, there are also further problems imposed by constraints on the sale of goods.  In markets like those for human organs there will be an entire class of would-be providers of goods that are removed from the market by the constraint.  Anyone who is willing to sell their organs, but not donate them, is removed from the market by the constraint, and is thereby removed from the matching problem analysed in “market design”.

    There are two aspects of great value in the work of the present Nobel prize winners.  The first is to allow them to alleviate the damage done by government intervention to some degree, by improving the allocation of goods under artificially imposed constraints.  The second is in demonstrating that even with this optimal solution under the constraint, the situation is still worse than would arise if these outside constraints were not imposed by governments in the first place.  Proper interpretation of the field of “market design” shows that it provides a second-best outcome in cases where the best approach — the free market — has been peremptorily removed by government intervention.

    References

    Gale, D. and Shapley, L.S. (1962) College admissions and the stability of marriage. American Mathematical Monthly 69(1), pp. 9-15.

    Ritter, K. And Wiseman, P. (2012) Americans Roth and Shapley win Nobel economics prize for studies on markets and match-making. Star Tribune, 15 October 2012.

    Roth, A.E. (1982) The economics of matching, stability and incentives. Mathematics of Operations Research 7(4), pp. 617-628.

    Roth, A.E. (2008) What have we learned from market design. The Economic Journal 118, pp. 285-310.

    Roth, A.E. (2012) Repugnance as a constraint on markets. Journal of Economic Perspectives 21(3), pp. 37-58.