Robert Nozick, The Refutation Of Rational Choice, Etc.

"Robert Nozick has a unique place in the annals of rational choice theory: he refuted it." -- Ian Hacking (1994)

My reaction, when reading this, was, "What?" Hacking is referring to a paper by Robert Nozick¹ on Newcomb's Paradox. I'm fairly sure I've read something about this paradox, but I had to look it up.

Suppose there exists a psychic that has shown themselves to be extremely reliable in their predictions. And the psychic has presented you with a choice, based on one of their predictions. You are presented two boxes, one transparent and one wrapped such that you cannot see the contents. The rules are that you can take either:

• Just the opaque box, or
• Both boxes.

The transparent box contains $1,000, as you can plainly see. If the psychic has predicted you will pick just the opaque box, they have placed $1,000,000 in it. If they have predicted you will pick both boxes, they have ensured that the opaque box contains nothing. The prediction has been made, and the boxes have been sealed. You know all these conditions but not what the prediction was. What should you do?

Apparently many initially are very decided on what they would do. But people split half-and-half on what that is. Anyways, Hacking states that this example shows that two principles of rational decision-making are not necessarily consistent². I guess he is correct, and I'm in no position to challenge that this is of philosophical interest³. But, since no such psychic can exist, I find other examinations of rational choice theory of more practical import.

By the way, I want to give a qualified defense of Stephen Metcalfe's comments in Slate on Nozick's Wilt Chamberlin example⁴. Strictly speaking, Metcalf's confusion about which Keynes comment was on which Hayek book is irrelevant to these comments later in the article⁵. And I accept that he doesn't describe the logic of Nozick's argument⁶. Neither did I. It is perfectly legitimate to argue that the rhetorical force of the argument comes from elements of the argument extraneous to its strict logic. And that is what Metcalf does⁷.

Footnotes

1. Nozick's "Reflections On Newcomb's Paradox" (in Knotted Doughnuts and Other Mathematical Entertainments (ed. by M. Gardner), W. H. Freeman, 1986).
2. Choose dominant strategies. Maximize mathematical expected utility.
3. I find Wittgenstein perennially fascinating.
4. Metcalf's Slate followup is here.
5. So is the fact that Nozick was smoking dope during the period in which he wrote Anarchy, State, and Utopia; I was startled to find he mentions in his book his experiences while under the influence. More by Brad DeLong on Nozick is here. Even more can be found in the Delong's blog archives.
6. By the way, Yglesias is mistaken in concluding, "Since as best I can tell nobody does hold such a [patterned] theory [of distribution]". Nozick explicitly states that marginal productivity gives such a patterned theory. Nozick is confused, since marginal productivity, correctly understood, is a theory of the choice of technique, not a theory of distribution.
7. Although I am not convinced appealing to guilty regret over the history of race relations in the United States has anything to do with Nozick's rhetoric.

Really, Really Free Market

I stumbled upon this idea recently. Not that I've ever physically seen such a market.

Elsewhere

• Alejandro Nadal asks, "Whatever happened to stability analyisis?" (h/t: Brad DeLong).
• A blogger with the pseudonym of "Lord Keynes" critiques Austrian Business Cycle Theory, based on Sraffa's demonstration of the non-uniqueness of the "natural" rate of interest in an intertemporal equilibrium.
• Jayati Ghosh provides access, from here, to an essay surveying Michal Kalecki's contributions to development economics.

A Popular Exposition Of Post Keynesianism

I have stumbled across a commentator, Tim Bending, at Open Democracy has been explaining some practical implications of Post Keynesianism. I particularly like this exposition of the theoretical incoherence of marginal productivity as a theory of the distribution of income.

Numeraire-Free Tests Of The Labor Theory Of Value

A reminder to my self - the following article belongs on this list.

• Mariolis, Theodore and George Soklis (2011) "On Constructing Numeraire-Free Measures of Price-Value Deviation: A Note on the Steedman-Tomkins Distance" Cambridge Journal of Economic, V. 35, N. 3: 613-618.

Three Routes To Choice

A theme of this blog is the incorrectness of the neoclassical textbook description of how agents choose. The assumptions of this view can be stated as:

1. An agent knows the complete list of choices from which they must select.
2. Given any two elements from this space of choices, the agent knows whether one of these elements is not preferred to the other.
3. Any element from this space is not preferred to itself.
4. The ranking obtained from the preference relation is transitive.
5. If the space of choices is a continuum, a certain continuity assumption must hold for the preference relation so as to rule out lexicographic preferences.

These assumptions supposedly imply the claim that utility attains at most an ordinal measurement scale level¹. And they allow one to derive the demand for consumer goods and the supply of factors of production.

Economists have transcended this framework. I have previously pointed out models of agents as consisting of multiple selves. I think this approach exhibits a consilience with theories in, for example, cognitive psychology. I have recently stumbled upon two other ways of modeling choice, generalizing the textbook view to an approach more consistent with empirical evidence from behavioral economics and that cannot be justifiably characterized as "irrational".

Nadeem Naqvi has developed an approach of incorporating tertiary information into choice. In the outdated neoclassical theory, one might represent the relationship y is not preferred to x for agent i by:

x R_i y

Naqvi and his colleaques introduce the relation R_i(V_i^j), where V_i^j is the background set for agent i. Parametric variation in the agent’s background set can alter the agent’s preferences. That is, one can have, for l ≠ m:

x R_i(V_i^l) y

and

y R_i(V_i^m) x

One interesting consequence of this modeling strategy is that racial discrimination is formally consistent with Pareto optimality. This "is a surprising, though serious, indictment of relying exclusively on the Pareto principle in social evaluation."

Gul and Pesendorfer consider choice among menus. They consider an agent who is a vegetarian for health reasons, but who is tempted to choose hamburgers, if available. In choosing a restaurant at noon, they would prefer a restaurant with hamburgers on the menu. But in choosing in the morning a restaurant to visit at noon, they will select one with an all-vegtable menu. I hope you can see how this approach allows one to analyze time-consistency of choices.

How long do you think before such approaches are presented in mainstream textbooks in widespread use?

Footnotes:
¹ Nominal, ordinal, interval, and ratio are well-known measurement scale level, where a level is defined up to a set of transformations. I find curious the claim that the expression of the marginal rate of transformation as a ratio of marginal utilities is consistent with an ordinal scale. Mirowski, in More Heat Than Light has also raised questions about the claim that utility only attains an ordinal scale level. I recently stumbled upon Mandler (2006), where he suggests, not necessarily for related reasons, utility be considered to attain a measurement scale level between ordinal and interval.

References

• George A. Akerlof and Rachel E. Kranton (2010) Identity Economics: How Our Identities Shape Our Work, Wages, and Well-Being, Princeton University Press (TO READ).
• Arian Berdellima and Nadeem Naqvi (2011) "Existence of a Pareto optimal social interaction with non-binary preferences".
• Frank Gul and Wolgang Pesendorfer (November 2001) "Temptation and Self-Control", Econometrica, V. 69, N. 6: 1403-1435.
• Michael Mandler (September 2006) "Cardinality versus Ordinality: A Suggested Compromise", American Economic Review, V. 96, N. 4: 1114-1136.
• Nadeem Naqvi (2010) "On Non-binary Personal Preferences, Economic Theory and Racial Discrimination".

Play It Cool, Daddy-O

1.0 Introduction "Is Von Neumann Square?" is one of my favorite titles for an article in economics¹. This post is about a case in which Von Neumann is more hep². Sraffa’s book presents a succession of models in which, after the second chapter, the system of price equations have one degree of freedom. This is usually taken to be a trade-off between wages and the rate of profits. Once the distribution of the surplus product is exogenously specified, prices are determined. Some, such as Michael Mandler and Paul Samuelson, have criticized Sraffian economics on the basis that this number of degrees of freedom is arbitrary. Cases can arise in which the system of price equations has either more or less than one degree of freedom. This post illustrates a case in which more than one degree of freedom exists. 2.0 The Example 2.1 Technology and Quantity Flows Consider a very simple economy in which laborers produce corn from seed corn on lands of definite types. Two types of land are available. Assume that this economy has 100 acres of land of each type available. Two Constant-Returns-to-Scale processes are known for producing corn. As shown in Table 1, each process requires inputs of a single type of land, as well as labor and seed corn. The technology is such that the order in which types of land will be rented can be read off directly from the technology. As I have previously pointed out, this is not a general property in long period models analyzing rent. I think this special case property, however, is not what drives the existence of possibly more than one degree of freedom.

Table 1: The Technology

	α Process	β Process
Labor	1 person-year	1 person-year
Type I Land	1 acre	0 acre
Type II Land	0 acre	1 acre
Corn	1/5 bushels	1/4 bushels
Outputs	1 bushel corn	1 bushel corn

Under the assumptions, anywhere from zero to 200 bushels of corn can be produced as gross output in this economy. Assume that the gross output of this economy is 100 bushels of corn. Then cost-minimizing firms will cultivate all of type I land, and all of type II land will lie fallow. 2.2 The Price System For stationary-state prices, no process can earn pure economic prices. This condition imposes the following inequalities:

(1/5)(1 + r) + ρ₁ + w ≥ 1

(1/4)(1 + r) + ρ₂ + w ≥ 1

• w is the wage (bushels per person-year), paid at the end of the year
• r is the rate of profits
• ρ1 is the rent (bushels per acre) on type I land, paid at the end of the year
• ρ2 is the rent (bushels per acre) on type II land, paid at the end of the year

An equality applies for any process in use. Land of a given type can be modeled, in an alternative specification of the technology, as jointly produced at the end of the period from the inputs of labor, seed corn, and that type of land³. As long as less than 200 bushels of corn are produced, at least one type of land will pay no rent:

ρ₁ ρ₂ = 0

2.2.1 First Special Case Consider what would happen if the gross output was infinitesimally less. Both types of land would be in excess supply. The rent on both would be zero:

ρ₁ = ρ₂ = 0

The solution in this case is:

0 ≤ r ≤ 4

w = (1/5)(4 - r)

Only type I land is cultivated. The number of processes in use is equal to the number of produced commodities, that is produced goods with a positive price. The system of price equations has one degree of freedom.

(1/5)(1 + r) + ρ₁ + w = 1

(1/4)(1 + r) + ρ₂ + w > 1

2.2.2 Second Special Case Consider, however, what would happen if the gross output was infinitesimally more. Both types of land would be cultivated. Type I land would not be able to produce all the output quantity needed for the requirements for use, and it would have a positive rent:

ρ₁ > 0

Type II land would be in excess supply, and it would have a rent of zero.

ρ₂ = 0

The price system becomes:

(1/5)(1 + r) + ρ₁ + w = 1

(1/4)(1 + r) + ρ₂ + w = 1

The solution is:

0 ≤ r ≤ 3

w = (1/4)(3 - r)

ρ₁ = (1/20)(1 + r)

Two produced commodities with positive prices exist: corn and the first type of land. And two processes are activated. 2.2.3 The Case With Two Degrees of Freedom But type II land does not need to be cultivated in the case under consideration. Thus, the costs of cultivating type II land can exceed the revenues, and the rent on Type I land is not determined by the price equations. Only the first equation in the system of equations for prices need obtain.

(1/5)(1 + r) + ρ₁ + w = 1

The second process is still characterized by an inequality:

(1/4)(1 + r) + ρ₂ + w ≥ 1

This system has the solution:

0 ≤ r ≤ 4

0 ≤ ρ₁ ≤ (1/20)(1 + r)

ρ₂ = 0

w = (1/5)(4 - 5ρ₁ - r)

Figure 1 illustrates one projection of this solution into two dimensions. The lines closer to the origin are drawn for a higher rent on the first type of land.

Figure 1: Variation in the Wage-Rate of Profits Frontier with Rent

3.0 Conclusions I am loath to argue that the extra degree of freedom in this example is negligible since it arises only for a knife-edge. If the quantity produced is a hair larger or a hair smaller, the input-output matrices for commodities with positive prices are square. But in a larger model, the quantity produced is a choice variable. I also don't see why Sraffian models must not have more than one degree of freedom. Footnotes ¹ If I’ve actually read this article, it must have been in a reprint in some collection. ² Some posts take me a while to write. I began this one the day after Arthur Laurents died. ³ I don't here show the derivation of rent from such a model. References

• Christian Bidard (1986) "Is Von Neumann Square?" Journal of Economics, V. 46: pp. 407-419.
• Michael Mandler (20xx) "Sraffian Economics (new developments)" New Palgrave, 2nd edition.

Austrian Welfare Economics Confused

In my critique of Austrian Business Cycle Theory, I cite some critiques of the Austrian school. Hill (2004) and Gloria-Palermo & Palermo (2005) critiques I do not cite.

Palermo and Palermo focus on how Austrian school economists reach normative conclusions. They put aside the influence of values in, for example, choosing the questions one addresses in one's positive analysis. For Austrian school economists, the idea of coordinated plans acts as a bridge from their positive theory to their normative claims. A state in which all agent's plans are coordinated is thought to be a desirable state by Austrian school economists. They claim that a market system has a tendency towards such a state without ever reaching it. Since then market systems are always in an undesirable state in which some agents' plans are mutually inconsistent and uncoordinated, why do Austrian school economists, in their nascent normative analysis, not conclude that market systems are undesirable?

• Greg Hill (2004). "From Hayek to Keynes: G.L.S. Shackle and Our Ignorance of the Future". Critical Review.
• Sandye Gloria-Palermo & Giulio Palermo (2005). "Austrian Economics and Value Judgements: A Critical Comparison with Neoclassical Economics". Review of Political Economy, V. 17, N. 1 (Jan.): pp. 63-78.