September 09, 2012

Pareto at Melos

Attention conservation notice: Advertises writings of economic theorists, utterly detached from the real world, as part of a long-running argument among academic bloggers.

Because Brad DeLong wants to revive a discussion from two years ago about "Hobbesian" tendencies in economics, I am reminded of a truly excellent paper which Brendan O'Connor told me about a few months I ago:

Michele Piccione and Ariel Rubinstein, "Equilibrium in the Jungle", Economic Journal 117 (2007): 883--896 [PDF preprint]
Abstract: In the jungle, power and coercion govern the exchange of resources. We study a simple, stylized model of the jungle that mirrors an exchange economy. We define the notion of jungle equilibrium and demonstrate that a number of standard results of competitive markets hold in the jungle.

The abstract does not do this justice, so I'll quote from the introduction (their italics).

In the typical analysis of an exchange economy, agents are involved in consumption and exchange goods voluntarily when mutually beneficial. The endowments and the preferences are the primitives of the model. The distribution of consumption in society is determined endogenously through trade.

This paper is motivated by a complementary perspective on human interaction. Throughout the history of mankind, it has been quite common (and we suspect that it will remain so in the future) that economic agents, individually or collectively, use power to seize control of assets held by others. The exercise of power is pervasive in every society and takes several forms. ...

We introduce and analyse an elementary model of a society, called the jungle, in which economic transactions are governed by coercion. The jungle consists of a set of individuals, who have exogenous preferences over a bounded set of consumption bundles (their capacity to consume is finite), and of an exogenous ranking of the agents according to their strength. This ranking is unambiguous and known to all. Power, in our model, has a simple and strict meaning: a stronger agent is able to take resources from a weaker agent.

The jungle model mirrors the standard model of an exchange economy. In both models, the preferences of the agents over commodity bundles and the total endowment of goods are given. The distribution of power in the jungle is the counterpart of the distribution of endowments in the market. As the incentives to produce or collect the goods are ignored in an exchange economy, so are the incentives to build strength in the jungle.

We define a jungle equilibrium as a feasible allocation of goods such that no agent would like and is able to take goods held by a weaker agent. We demonstrate several properties that equilibrium allocation of the jungle shares with the equilibrium allocation of an exchange economy. In particular, we will show that under standard assumptions a jungle equilibrium exists and is Pareto efficient. In addition, we will show that there exist prices that 'almost' support the jungle equilibrium as a competitive equilibrium.

Appreciating this requires a little background. There are multiple arguments to be made on behalf of the market system. The one which the mainstream of the discipline of economics likes to emphasize, and to teach, is the "first fundamental theorem of welfare economics". Assume some obviously false conditions about what people want, and still more obvious falsehoods about the institutions they have. (There need to be competitive markets in literally everything anyone might want, for instance.) Then let people trade with each other if they want to, and only if they want to. The market comes to equilibrium when no one wants to trade any more. This equilibrium is a situation where nobody can be made better off (by their own lights) without someone else being made worse off. That is, the equilibrium is "Pareto optimal" or "Pareto efficient". (Actually, the theory almost never considers the actual dynamics of the exchange, for good reasons; it just shows that every equilibrium is Pareto optimal*.) This theorem gets invoked a lot by serious members of the profession in their writings and teaching. I will leave supporting citations and quotations for this point to Mark Blaug's "The Fundamental Theorems of Modern Welfare Economics, Historically Contemplated" (History of Political Economy 39 (2007): 185--207). Suffice it to say that many, I suspect most, economists take this to be a strong argument for why market systems are better than alternatives, why market outcomes should be presumed to be good, etc.

A conventional assault on this is to argue that the result is not robust — since we know that the premises of the theorems are quite false, those theorems don't say anything about the virtues of actually-existing markets. Then one has mathematical questions about whether the results still hold if the assumptions are relaxed (generically, no), and empirical questions about processes of production, consumption and distribution.

What Piccione and Rubinstein have done is quite different. They have shown that the same optimality claims can be made on behalf of the most morally objectionable way of allocating resources. "The jungle" takes the horrible message of the Melian dialogue, that "the strong do what they can and the weak suffer what they must", and turns it into the sole basis of social intercourse**. And yet everything which general equilibrium theory says in favor of the Utopian market system is also true of the rule of force. In this hybrid of Hobbes and Leibniz, the state of nature is both just as repugnant as Hobbes said, and yet also the best of all possible worlds.

Piccione and Rubinstein's paper undermines the usual economists' argument from Pareto optimality, because it shows not just one or two horrible Pareto optima (those are very easy to come up with), but a horrible system which is nonetheless Pareto-efficient. Of course, there are other cases to make on behalf of markets and/or capitalism than the welfare theorems. (But: the jungle is fully decentralized; free from meddling bureaucrats or improving intellectuals; provides strong incentives for individual initiative, innovative thinking, and general self-improvement; and of no higher computational complexity than an Arrow-Debreu economy.) I should add that anyone who actually grasps the textbook accounts of welfare economics should certainly be able to follow this well-written paper. They will also benefit from the very sensible concluding section 5.2 about the rhetoric of economists.

*: The second fundamental theorem is that, roughly speaking, every Pareto optimum is a competitive equilibrium, attainable by a one-time transfer of goods. This does not hold for "the jungle" (section 4.2 of Piccione and Rubinstein).

**: Hobbes — this was originally a conversation about Hobbes — was, of course, highly influenced by Thucydides, going so far as to translate The Peloponnesian War. (His version of the line is "they that have odds of power exact as much as they can, and the weak yield to such conditions as they can get".)

The Dismal Science

Posted at September 09, 2012 22:29 | permanent link

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