Saturday, September 29, 2007

Liberalism vs. Pareto?

Let’s swear off the depressing subject of current events for a while. I’m working through Andrew Schotter’s Free Market Economics, a thought-provoking (and sometimes simply provoking) attack on arguments for free markets, an immanent critique that largely accepts the arguments on their own terms. Professor Schotter served on my dissertation committee at NYU; I was and am very impressed with his professional work, and know first hand that he’s not someone to be dismissed quickly. Hence I am giving his book careful study and expect it to be very fruitful.

Early on, in a chapter reviewing others’ criticisms of free market arguments, he discusses an argument attributed to Nobel Laureate Amartya Sen, although I think it is much older, an alleged contradiction between the Liberal standard of respect for individual rights and the Pareto criterion by which state of affairs a is preferable to state b if no one is made worse off by a move from a to b and at least one is made better off.

Sen’s paradox is this: Pareto optimal outcomes may be inconsistent with liberal respect for individual rights. As an illustration, suppose we have two people, Archie and Betty, and a risqué book, Lady Chatterly’s Lover. Consider three possible states of affairs: in state a, only Archie reads it, in state b, only Betty reads it, and in state c, no one reads it. Puritanical Archie has c as his most preferred state and a as his second, since he supposes he at least has the moral sense to resist being corrupted by the book. Betty, OTOH, has state a as her most preferred, since she doubts his resistance is so strong and believes he’ll lighten up after reading it. And if not that state, then at least she’d like to read it.

To recap, for A, c > a > b. For B, a > b > c. (If anyone can tell me how to insert preference operators into text, instead of inequality signs, please let me know: big reward!)

According to Schotter, Sen poses his paradox this way: suppose we use a liberal standard to compare state a vs. state c (only Archie reads it vs. no one reads it). By this standard, A’s preference must be given priority, so c > a. I gather the argument is that we ought not compel Archie to read it.

Next, let’s use the same standard to compare states b and c. Here B’s preference must be given priority, so b > c, and Betty should read it. Presumably we shouldn’t constrain Betty.

Sen then notes that together these give us the ranking b > c > a, and so b is the preferred state by the liberal criterion. However, going from state b to state a is a Pareto improvement! Hence, the two standards are in conflict. And worse, it’s apparently possible to make everyone better off by rejecting the liberal standard: we force Archie to read it and prevent Betty from reading it.

This looks like a puzzle, all right, but it isn’t clear to me what the puzzle is. The lesson that was always hammered home on me in my graduate training at Montana State and NYU is that we need to specify an initial endowment of rights; only with respect to this can a Pareto improvement be defined. Hence, for example, Coase’s emphasis on the crucial importance of the distribution of property rights. The usual illustration is an Edgeworth box. There are many Pareto optima, but the notion of a Pareto improvement is meaningless until an initial endowment has been defined. Once that’s done, any basket within the so-called lens is a Pareto improvement, and, if it’s not an optimum, it defines a new, smaller lens defining further Pareto improvements. The crucial point is that a Pareto improvement can be defined only with respect to an initial distribution of rights.

My first question for Sen’s story is "what are the rights?" Does B have the right to choose to read Lady Chatterly or not? If yes, why is a an option under consideration? If no, why is b an option under consideration? How can these both be options under a single distribution of rights? So far as I can see, states a and b are mutually excluded under a single set of rights. Hence, the alleged contradiction stems from a failure to specify a single set of rights by which a Pareto improvement can be defined.

In the Edgeworth box setting, I think the equivalent is to compare two initial endowments that generate two non-overlapping lenses. Let (0, 0) for A be the southwest corner of the box, and for B the northeast corner. Draw a lens defined in the usual way, and call the endowment that generates this lens b. Then pick a point on the interior of this set, call it a, and note that everyone strictly prefers it to b. Next pick any point that lies outside the lens and strictly to the NE of a, and call it c. Note that A prefers c to a and B prefers b to c. Are we surprised that a move from b to a is a Pareto improvement, and yet A prefers c to a and B prefers b to c? What’s the puzzle? We’re starting from two different endowments, i.e. two sets of property rights in making the comparisons. (Exercise for reader: diagram this. It’s a lot simpler than it sounds in words.) (Appeal to reader: If anyone can tell me how to easily develop graphics of this, instead of tangled verbiage, please let me know...big reward!)

This problem is important, because if the Sen-Schotter analysis is correct, then it's possible that by violating individual rights we might make everyone better off. And if I am correct, Sen and Schotter have made a mistake in their analysis, presumably without realizing it, by specifying two sets of mutually contradictory rights and treating them as one.

And of course, if a really is a Pareto improvement, the liberal standard allows A and B to contract to achieve it. Archie agrees to read the book if Betty agrees to not read it. And no liberal objects. Again, any serious attention to the distribution of rights makes this whole paradox seem misplaced.

My conclusions: First, the alleged paradox stems from a failure to clearly specify rights, and does not show a conflict between a liberal insistence on rights and the Pareto criterion. Second, it’s surprising that intelligent economists such as Sen and Schotter seem to have missed this. It’s not as though no one has said this sort of thing before, since the lessons of Israel Kirzner, Ron Johnson, Ronald Coase, Jack Hirshleifer, Steven Cheung, and many others (Vilfredo Pareto, even!) have always been available, and even right under their noses (Kirzner’s office was two doors down from Schotter’s).

Sometimes the unforeseen contingencies shouldn’t have been so hard to see.

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