The following question was posed by a member of the list. Another pointed out my doubts about the use of formalizations of various kinds for explicating, predicting or justifying much of what goes on in litigation:
> Insofar as the realm of law is concerned, a basic question is: Do >bivalent logic and bivalent-logic-based probability theory provide >adequate tools for a formalization of legal reasoning? In my view, legal >reasoning is much too complex to lend itself to an analysis within the >conceptual structure of bivalent-logic and bivalent-logic-based >probability theory. A few comments: 1. References to the "law," or "legal reasoning" are much too broad to be useful. Interestingly, though, within such broad referents, standard probability theory has played a remarkably important role. It is, in the guise of statistics, at the heart of microeconomics and econometrics, for example, both of which have transformed certain areas of the law, such as antitrust and discrimination law of various kinds. Rough sets and fuzzy sets, by contrast, have played no role at all. Standard probability measures also are critical in such matters as apportionment of the House of Representatives, and the distribution of benefits under welfare programs of various kinds. 2. If the referent is limited to fact finding for the purposes of litigation, all of the above matters may find themselves the focus of litigation, and the same answer would be given. 3. In addition, experts are standardly used at trial today, but they have to be qualified as testifying on the basis of "scientific or expert" knowledge. What that might mean is problematic, to be sure, but an important component is standard controlled studies, all of which are beholding to probability theory in one manner or another, of course. Again, whether for good or ill, no one to my knowledge has ever qualified an expert on the basis of scientific or expert knowledge gained or tested through techniques based on rough or fuzzy set theories. I understand that such theories are critical to certain manufacturing activities, and it is easy to how such matters might become the subject of litigation. Were they, experts in engineering in fields in which fuzzy or rough sets matter plainly could be qualified. In any event, I am here just describing the present lay of the land. 4. The issues to which Peter Tillers's references are relevant involve the use of algorithms to explain or justify general approaches to fact finding within litigation. Here there has been a remarkably consistent failure of algorithmic approaches to be of any great help. The formal structure of the evidentiary process at trial simply doesn't map easily onto any formal approach. For example, standardly "elements" must be proven to a predetermined standard of persuasion--typically a preponderance of the evidence in civil cases and beyond reasonable doubt in criminal cases. At the same time, trial is supposed to minimize or equalize errors in civil cases and skew errors to protect innocents in criminal cases. These two points are plainly at odds with each other if the standard of persuasion is given a conventional probabilistic interpretation. Similarly, efforts to explain the evidentiary process as Bayesian run up against formal problems such as computational complexity, failure to specify the probability space until the end of the trial (and thus all evidence is old evidence), and possible introduction of new hypothesis all the way up to the moment of decision (thus requiring a reconfiguration of the probability space). And of course, the only plausible Bayesian approach at trial is subjective Bayesianism, which is not promising in general in terms of truth generation. 5. This has led some people (like me) to conclude, as Prof. Tillers rightly suggests, that the track record of formal explanations of general evidentiary matters (outside of expert areas) at trial is not terribly good. It has also led theorists to consider the relationship between things like conventions concerning burdens of persuasion and the rest of the procedural setting in which they are embedded. From that perspective, what appears to emerge is that trials generate comparative stories over which decision is made, or from which a third story is derived, to explain the events in question. The agreed upon explanation of the events is then mapped onto the decision possibilities (and here there is some considerable support from the psychological literature that this is what jurors do). 6. The procedural setting at trial and the comparative nature of the proof process explain to a considerable degree why the formal arguments this list is having do not seem to map directly onto juridical fact finding issues. First, it is simply not the case that the critical decision typically is "Did X cause Y or not." Rather, is it "which of these stories, one involving causation, and one not, is relatively more plausible." In an employment discrimination case, the functional question is: Was the employee more likely fired because of discrimination or incompetence, and not: Was the employee fired because of discrimination or not? In the raincoat hypothetical, the parties would formulate their competing hypotheses, and present them to the fact finding. Many have complained that the problem is insufficiently formulated to answer; this is the reason it is insufficiently formulated to be of interest from the legal point of view. One needs to know what claims, for and against, are being made, what the evidentiary base is, and so on. A similar, slightly different, point is true of the former hypothetical that I believe was offered to show that fuzzy sets may have significance for legal decision making, which was, if memory serves, the assertion that somebody was "tall." Standing alone, that might very well call for a fuzzy set interpretation. But, if it matters, it will never stand alone at trial. If a witness testifies that a person, was "tall," and what "tall" means matters, it will be clarified through examination and cross-examination. "How tall? I really don't know. More than 7 feet? No. Less than five feet? No. About half way in between? Well, maybe, I really don't remember. Taller than you? Yes, maybe an inch or two. How tall are you? Six feet. So, maybe the person was about six fee two inches? Yes, probably." And so on. Again, if it matters, further comparisons can be made. Taller than me, not as tall as you, and so on. Now, maybe this can be given a fuzzy set interpretation, just as it can be given a conventional probabilistic interval interpretation, but neither matters. Neither assists the process of trial or enlightens us about the meaning of the testimony. Both would be interesting but epiphenomenal. 7. Thus, I agree with Prof. Zadeh that the legal system presents problems much too complex to be dealt with through standard applications of probability theory or statistics. However, it has responded to that problem in ways that make it doubtful that any so far articulated formalization (such as fuzzy or rough sets) is of much use, either. The error here is the belief implicit in the comment quoted at the beginning of this email that the law must choose over various formalizations, and that "legal reasoning" has some need of or would benefit from "formalization." It is very difficult to prove a negative, but this is probably wrong. Of course, a useful formalization would be nice, but, as briefly laid out above, there don't seem to be any candidates. Needless to say, I hope, the extension of this point does not include basic attributes of rationality, some of which could be offered as counter examples to the irrelevancy of formal approaches, such as the use of syllogistic reasoning and the like. I take it that it is plain that that is not what is under discussion, although I think it an interesting philosophical question how clear a demarcation could be drawn here. In any event, the question is the general structure of the evidentiary process, rather than the discrete responses any individual thinker may have to any particular datum. 8. Having said all this, many legal theorists, including I believe Prof. Tillers, and certainly myself, continue to explore the boundaries between trial procedure and formal reasoning. The positions we presently occupy are not dogmatic but instead realistic. I would be very excited to see a demonstration that some formal method was useful at trial (in the sense I mean those terms). None of the examples so far, either on this list or in the literature, come close to such a demonstration, largely because they don't involve relevant problems or because they do not account for the actual procedural setting at trial, as discussed above. Sorry about the length, but these ideas have been percolating as the list has discussed various related things. Best regards, Ron Ronald J. Allen Wigmore Professor of Law Northwestern University Phone: 312-503-8372 Fax: 312-503-2035
