Incommensurable choices and the problem of moral ignorance.

• Author: Katz, Leo
• Position: Symposium: Law and Incommensurability

If I cannot decide between A and B, that would seem to show that I am indifferent between them. But as Joseph Raz famously demonstrated in The Morality of Freedom(1) it does not show that at all. His demonstration basically consisted of pointing to a feature of such situations that previously had been overlooked completely. If I cannot make up my mind between a Toyota and a Honda, it certainly looks as though the reason I am dithering is that I am nearly indifferent between them. But consider, said Raz, that I would have no problem making up my mind between one such Honda and another such Honda that happened to be selling for a few dollars less. If I were truly indifferent between the more expensive Honda and the Toyota, Raz observed, then I should no longer be indifferent between the cheaper Honda and that self-same Toyota: I should prefer the cheaper Honda. But since I find choosing between the cheaper Honda and the Toyota just as hard as choosing between the more expensive Honda and the Toyota, something else must be going on.

What exactly is going on in such a case is, of course, quite mysterious. Hence this Symposium.(2) Everyone would, I think, agree that what is going on has something to do with the fact that I find the cheaper Honda easy to compare with the more expensive Honda, but that I find either of the Hondas quite hard to compare with a Toyota--they are just so different. They are, it seems, incommensurable. My being unable to decide between the two cars thus seems not to stem from my being in equipoise between them (otherwise a slight drop in the price of the Honda immediately would break the tie), but from my being unable to compare them properly.

In the first Part of this Article, I will try to show that the roots of this mysterious-seeming incommensurability phenomenon are often very mundane and that the problem of what to do about incommensurable choices is therefore often very easy to solve. To be more precise, I will try to show that things have a way of seeming incommensurable for no other reason than that the chooser happens to be fairly uninformed about them. Once his ignorance is dispelled--as a result of nothing more than a bit of sustained investigation and reflection--the incommensurability generally will disappear. In the remainder of the Article, I will pursue some questions that arise out of this: What is one to do if one has not yet been able to come by the information or the insight that would make the incommensurability disappear? And how bad is it if one gets things wrong?

1. HOW IGNORANCE LEADS TO INCOMMENSURABILITY

   The idea that incommensurability is simply a manifestation of ignorance is not original with me. Donald Regan has taken a line somewhat like this in his extended essay on Raz's book.(3) Here, I will pursue the point farther than he does, as well as pursue the further interesting questions to which it gives rise. The best way to explain what I have in mind is with an example. Suppose we face the task of comparing two irregularly shaped pieces of paper as to their size. One of these pieces of paper resembles in outline the State of Texas, the other the State of Idaho. To look at them, it seems possible that they are equal in area, or that one of them is larger. There seems no easy way to tell which is the case. Suppose now there exists a third piece of paper, which in fact has the same shape as "Idaho," but on a slightly smaller scale. We are now finding ourselves in a situation that has all the earmarks of incommensurability. We are unable to choose as between Texas and Idaho which is larger. We have no trouble deciding that "big" Idaho is larger than "small" Idaho. Nevertheless, this does not mean that we are able to choose between Texas and .small" Idaho as to which is larger. The reason for this perceptual kind of incommensurability seems to be the relative ease with which we can compare the two Idaho shapes and the difficulty of comparing either of those shapes with the Texas shape. Note, however, that the incommensurability we have encountered here can be dispelled relatively easily. All we need to do is to stop trying to make the judgment by the eyeballing method and resort to more advanced measuring instruments instead. The incommensurability here is simply the result of ignorance: our inability to do with the naked eye what we could easily do with some measuring tools. Dispel the ignorance and you have eliminated the incommensurability.

   In an implicit way, the law has, in fact, long recognized the intimate connection between incommensurability and ignorance. Consider the way the burden-of-proof rules operate in a civil case. Imagine a plaintiff who makes an allegation and backs it up with the meagerest of evidence. The defendant in turn denies it, offering no evidence whatsoever. Under such circumstances, a court is obliged to dismiss the case on the ground that the plaintiff has not met his burden of proof. Let us explore a little bit what it means to say here that the plaintiff has not met his burden of proof. It clearly does not mean that the defendant has by a preponderance of the evidence disproved the plaintiff's allegation. Rather, it means that the court has not been provided enough information to be able to decide which of the two sides is right. How should we think about the judge's inability to decide which side is right? Are we to think of him as being in equipoise between the two parties? Does the defendant win because the plaintiff has only managed to put the case into equipoise rather than the "50%-plus-a-smidgen" range that would entitle him to win? The burden-of-proof rules make it clear that the court's inability to choose between the two sides does not show it to be in equipoise: If such were the case, then the plaintiffs introduction of a mere scintilla of additional evidence would entitle him to a favorable judgment. It is quite clear, however, that much more is demanded of him. The burden-of-proof rules thus treat the judge's inability to decide as a sign of incommensurability rather than indifference.

   In probability theory too, the connection between incommensurability and ignorance long has been recognized. Somebody asserts a proposition, the truth of which I have no idea. I am unable--to put the matter with pedantic, but I think illuminating, clumsiness--to decide between two alternatives: (1) the proposition is true; and (2) the proposition is false. Does my inability to choose reflect that, given how little information I have on the matter, each alternative is equally likely? Although it is tempting to think so, that would lead to contradictions. The root cause of those contradictions turns out to be the fact that my inability to choose between the two alternatives reflects not "indifference" but "incommensurability."

   Consider the statement "Brian will win his next gamble." Not having any evidence whatsoever on the matter--not even knowing what kind of gamble is being contemplated--you might be inclined to consider yourself "indifferent" on the issue and assign a 50% probability to the possibility that Brian will win, and a 50% probability to the possibility that Brian will lose. Consider next the statement "Brian will win a million dollars in his next gamble." This statement, being more specific than the first statement, is less probable than the first statement. Nevertheless, since you have no evidence on the matter, you should consider yourself "indifferent" on the issue and assign a 50% probability to the possibility that Brian will win a million, and a 50% probability to the possibility that Brian will not. The result, of course, is that you end up in a contradiction. Because, in fact, you are not indifferent between the two possibilities, you are not truly in equipoise. The two alternatives are simply incommensurable.

   If I am right about the connection between incommensurability and ignorance, then there should be many cases in which previously incommensurable alternatives are rendered commensurable through the influx of additional information or insight. And indeed, there is no dearth of such cases. Every time a plaintiff backs his complaint up with evidence, he turns an incommensurable choice into a commensurable one. But those are admittedly very mundane, factual kinds of choices. What about incommensurable choices that have a heavier moral tinge to them? Are there examples here too of incommensurability being dispelled through insight or information? Let me suggest a few.

   1. Utility Measurement

      Economists and utilitarians used to be much bothered by a very basic kind of incommensurability: our inability to compare the happiness derived from our first one thousand dollars with the happiness derived from our last one thousand dollars. Intuitively, it seemed right to say that the latter conferred much less joy than the former. But no one felt that he had a truly secure grip on that comparison.

      That insecurity was especially apparent when one was asked to compare, say, the joy derived from having one's income jump from $10,000 to $20,000 with the joy derived from having one's income jump from $100,000 to $200,000. Those two kinds of joy seemed truly incommensurable. It was clear that the joy of seeing one's income rise from $100,000 to $200,001 was greater than seeing it rise from $100,000 to $200,000. Yet it did not therefore follow that that joy was greater than the joy of seeing one's income rise from $10,000 to $20,000.

      In the end, it turned out that our inability to compare these different quantities of happiness was much like our inability to compare the size of two irregularly shaped pieces of paper. They are incommensurable if we insist on settling the matter by eyeballing. They become commensurable once we resort to more refined technology. In the case of utility measurement, that technology was the Von Neumann-Morgenstern approach to constructing a cardinal utility function. By making the simple...