Sen’s Paradox replicated

Recall Sen’s èaradox. There are two agents Lewd and prude. Lewd likes to read pornography, Prude does not, but what really disturbs Prude is the thought that Prude is reading pornography and enjoying it. Similarly, while Lewd enjoys porn what would really get him off is the thought of Prude reading porn and being shocked. A liberal would consider each to have the right to do what he wishes so Lewd would read porn and Prude would not. Pareto would say this is an unacceptable outcome and propose a Pareto improvement in which Lewd is not allowed to read porn and Prude is forced to read porn. Both Lewd and Prude are happier so this is a Pareto improvement. Thus one can not be a Paretian liberal.

The point is that liberals like to think that they can be consequentialists too. That is that liberal rules lead to desirable outcomes and certainly, at least, to Pareto efficient outcomes (in which to make an agent happier some other agent must be made less happy so no Pareto improvement is possible). Now even if one agrees that liberal policies lead to good outcomes in the real world, Sen showed that the philosophical problem remains. Considering his hypothetical world, we see that we might have to decide if we consider liberty good as a means to the end of making people happy or good in itself.

Brad Delong (I think I can’t find it on his blog so no link) finds it hard to accept Sen’s world in which the only possibilities are compulsion or each acting alone without interacting with the other. He asked why don’t Lewd and Prude sign a contract in which Lewd promises not to read porn and Prude promises to read porn. Then the Optimal outcome is achieved via the liberal principal that the state should enforce contracts.

Personally, I am willing to accept the assumption that they can’t contract as much as I am willing to accept the assumption that they have weird preferences. However there is also a standard way to make private contracting ineffective – replicate the model.

Imagine a million prudes and a million lewd people. The prudes don’t want lewd people to read porn. The lewd people really really want prudes to read porn. A proper moral tone in which no one is reading porn and enjoying it is a public good for prudes. A hilarious world in which all prudes are being shocked by porn is a public good for lewd people. A Pareto efficient outcome would be for all prudes and no lewd people to read porn. This can not be achieved without compulsion because there is a collective action problem. Consider one of the many identical prudes P. P does not care if other prudes read porn. To read porn causes P 100 units of pain. For a lewd person to read porn causes P 1 of pain. Now consider lewd L. To read porn gives L 100 units of pleasure. For a prude to read porn causes L one unit of pleasure. The best contract for L and P is to leave each other free to choose. There is no set of prudes which can gain from contracting with L. There is no set of lewd people who can gain from contracting with P. There is a free rider problem. The immoral prude who shirks his or her duty to read porn leaving the whole burden of keeping lewd people from reading porn to the public spirited prudes who, sad to say, given the assumptions above don’t exist.

Now this example is very unrealistic, because people are totally selfish and incapable of shared sacrifice. However that is an assumption about preferences not about what contracts are allowed. Two agents can write a contract to achieve Pareto efficiency. 200,000,000 can’t or rather the contract is called the social contract and it’s particular clauses are called laws.

Prudes seem to positively enjoy collective action. In fact, as far a as I can tell that is the main fun of being a prude. Consider kiddie porn. I hate it. I think I would enjoy fighting the good fight against kiddie porn in community of anti kiddie porn activists (so long as we could keep the prudes out of our campaign). I am almost ready to claim that the problem is not that I am lazy and selfish but one of coordination. I am willing to note that even in the hypothetical case that I were not lazy and selfish there would still be a coordination problem.

My conclusion is that Sen’s claim does not require the extraordinary assumption that people can not contract. It holds if contracts are arrived provided the original model is replication a few million times.

Historical digression. Why have I been talking about “reading” porn on a web page even. If it’s like a book which you read, it can’t be porn right ? This is roughly the state of current jurisprudence (which is I admit more grammatical). Sen was writing just after an English court decided that “Lady Chatterley’s Lover” was not porn. In a name dropping digression from the digression, I heard Sen present Sen’s paradox to graduate students and he apologised profusely for his benighted generation born early enough to see judges who thought that “Lady Chatterley’s Lover” might be porn. I mean a bit preachy yes but porn ??? Why it is a classic. Clearly part of the Canon as defined by Microsoft Word which just corrected my spelling of