20 October 2003

Warning: This is yet another overly theoretical post.

   Professor Solum posted a solid summary of the "veil of ignorance" problem yesterday at his Legal Theory Blog.

How do parties behind the veil of ignorance deliberate? For the most part, legal theorists will want to leave the deliberative processes relatively untouched. Huh? By that I mean that unlike Rawls, legal theorists do not need to specify that the parties pursue some particular goal (maximimizing their share of the primary goods) but can leave the parties with the interests they have before the veil descends. Rawls specified a particular decision rule for the parties—the maximin rule—which required the parties to maximize the share of the primary goods that would be held by the worst-off group. Again, legal theorists may not need this very strong assumption about how the parties deliberate.

(emphasis removed for clarity). The hidden inquiry here—one that underlies a lot of law and economics interpretations, and one that I have a great deal of difficulty ignoring—is "how does one measure maximum utility?" The maximin rule is useful only in choosing between results within the same boundary conditions. There is another condition, however, that is best illustrated in gambling and theories of military deterrence, that may or should enter into the rule: the greatest-negative-excursion rule. This turns on "what is the minimally acceptable worst result?" For those not willing to reject Luttwak—which requires reading Luttwak in the first place, a burden I would not wish upon most of my enemies, because his writing is somewhat dubious in its integrity—an example from blackjack might be helpful.

Gambler A has an initial stake of $2500. He is sitting at a $5000-limit table with a $250 minimum. In order to pay for his hotel room for the night, he must walk away from the table with a minimum of $250 at then end of a multihand session, and does not know before a given bet whether he may quit after the succeeding hand. What is the maximum bet that he can afford to place on a given hand?

The immediate impulse is to think that the maximum bet must be either (current stake-$250) or (current stake-(2*$250)). But that is not correct, because the length of the game is unpredictable. The maximum bet that he can make is the table minimum ($250), because in an unpredictable-length game, he must assume that he could enter a string of losing transactions without an allowable exit. So long as the player cannot predict that his exit point will allow him to leave with better than his minimally acceptable result, he must act to "not play" to the greatest extent possible—unless he truly is a gambler, and therefore not a "rational actor" in the economic sense. The most-probable result is not the issue here; the issue is survival. Thus, the social justification for the billions spent on nuclear deterrence: the result of "failed deterrence" was considered so awful that the actual cost of maintaining "deterrence" became an almost irrelevant consideration, mineshaft gaps and all.

   Life insurance premiums are another example, because they are merely a bet that the particular individual's circumstances make it more favorable to purchase a grossly overpriced protection against an unpredictable event. Statistically, if one assumes that the actuarial tables define each individual's final circumstances, one cannot justify paying for life insurance; the pricing set based on those tables results in a hefty profit for the insurer. The key, though, is that the exit point cannot be predicted, and the worst acceptable outcome requires a greater payoff at death than the prospective purchaser can guarantee from current funds.

   It is also directly relevant to the veil of ignorance problem. So long as maximum utility is measured as a collective function, whether the rule of decision is maximin or otherwise, the result is going to be different than if maximum utility includes a minimum acceptable excursion as a boundary condition, or if maximum utility is measured as a sum of individual results rather than a field equation. In more symbolic terms, the minimum-acceptable excursion condition states that a discontinuity (exceeding of the boundary condition) in a single instance from 0 to i results in an invalid summation. That must then plug back in to the share of primary goods that decisionmakers purportedly strive for—because the decisionmaker must assume, at some level, that he or she might end up on the "short end of the stick" and therefore must have some idea of just how short that stick can be and still be acceptable. In real legal theory—if that is not an oxymoron—this is often clearest when considering burdens of proof: the shortest acceptable stick is a lot shorter under a "preponderance of evidence" standard than under a "beyond a reasonable doubt" standard, let alone a "scientifically proven" or "morally certain" standard.

   All of which is a roundabout way of saying that an unrestricted English Rule (in Solum's description, choice 4) is not a valid solution if one accepts nontrivial legal fees as the minimum bet in the dispute-resolution game, because it cannot adequately account for the minimum acceptable excursion. This is related to copyright law, because under the Copyright Act there is a modified English Rule in effect (see Fogerty v. Fantasy, Inc. and a practical application of the rule in Ellison), and somewhat less so under the Lanham Act (trademark law) and Patent Act.

   I clearly need more caffeine this morning.