Sunday, March 23, 2003

Does Posner Say What Simon Says?

A friend -- another knowledgeable observer (who I think wishes to remain anonymous) --, this extremely astute and knowledgeable friend & observer has confirmed my suspicion that (Richard) Posner (in his recent paper on evidence) does not say what (Herbert) Simon says. But in mentioning information theory in my earlier post I was not trying to delve into theories of "bounded rationality," which are now much in fashion. [For one interesting collection of papers about this topic, see G. Gigerenzer & R. Selten, BOUNDED RATIONALITY : THE ADAPTIVE TOOLBOX (MIT, 2001).] I wanted, instead, merely to get a handle on the type of "search" or "value of information" theory that Richard Posner embraces in his recent paper on evidence in litigation.

My knowledgeable friend's comment indirectly supports a hunch that I had had about Posner's theory making rational decisions about gathering evidence: Posner's theory of "search" is an application of EU theory, "expected utility" theory -- or MEU theory, "maximization of expected utility" theory; or, SEU, "subjective expected utility" theory; or, a bit redundantly: MSEU, "maximization of subjective expected utility" theory --, a theory that, in this context, would assert, I would think, that a rational decision maker will or should continue to invest in gathering new evidence or information only as long as the marginal (expected) benefit of gathering new evidence exceeds the marginal (expected) cost of doing so -- or, more precisely, only as long as (S)EMC ([subjectively-] expected marginal cost) of gathering new evidence does not exceed (S)EMB ([subjectively-] expected marginal benefit) of gathering additional evidence. {My notation is both unorthodox and crude, but ... you follow me, right, Dear Reader?}

Dear Reader, is this -- such talk about subjective expectations of marginal benefits and the like -- does such talk capture (roughly) the way Posner thinks about the problem of determining an appropriate individual or institutional "stopping point" for further investment in information or evidence? {N.B. There is the complication that in an institutional context -- e.g., a societal context -- we would need to determine whose (subjective) expectations count. But let's leave this little(?) complication aside.}

Here again is my principal argument about Posner's account of evidence in litigation: if Posner does indeed adhere to a simple and "classic" version of value of information theory, the sort of simple MEU theory that I have just tried to describe, then my original thesis holds: viz., the project of calculating benefits and costs of acquiring additional (unknown) information or evidence becomes more difficult -- and, in extremis, perhaps impossible; or, in any event, rather mysterious, a bit ineffable -- to the extent that new evidence contains "surprises," to the extent that new evidence routinely generates new hypotheses or produces mutations in previous hypotheses.

Glenn Shafer has pointed out that bits of evidence often function as "hints," that bits of evidence suggest previously unimagined hypotheses and refinements of existing hypotheses. [Here I must concede, Dear Reader, that Shafer's emphasis seems to be on the capacity of evidence to produce refinements of existing hypotheses rather than on its capacity or tendency to generate entirely novel hypotheses.] If one thinks that the suggestive, abductive, or hint-like character of evidentiary details is pronounced, very substantial, one must, at a minimum, concede -- yes? no? -- one must then concede the possibility that the ability to calculate -- even intuitively -- the probable costs and benefits of acquiring previously unknown information or evidence is limited, perhaps radically limited.

Consider the converse proposition: if one is able to identify the hypotheses about which there is uncertainty (and about which one would like to improve the quality of one's judgments & guesses), then one may (sometimes) be able to make some good guesses -- if one has some knowledge of the pertinent portion of the cosmos, if one has some pretty good "ontologies" at hand -- then one may be able to make better than random estimates about the knowledge-payoff that will result if one takes the time, trouble, and resources to examine particular sources of evidence and information that one had not hitherto examined. But this sort of calculation becomes more "problematic" if one thinks that the process of examining previously-unexamined sources of evidence and information will generate new hypotheses or cause original hypotheses to mutate. (And if one cannot predict such hypothesis-mutation -- to any extent -- then the project of making guesses and estimates about the value of new information becomes altogether inconceivable, no? -- a fact that suggests that human beings to have, must have, some way of guessing about the value or fruitfulness of the "surprises" that acquisition of new evidence might generate. Right? Or? [The moral of this last hedge: it is not my ambition here to turn us all into radical fact-skeptics. I just want to have a theory of evidence that is adequate to the way the world, the mind, and evidence work. In reality, of course, human beings sometimes do {seem to} have an ability to sense which lines of factual investigation are likely to prove fruitful. This sense, one would think, characterizes both good detectives and great scientists.])