Causes, Associations & Signs

Theories about the workings of inference from evidence perhaps fall into three groups:

1. probabilistic causality
2. associationism
3. semiotics

The first approach holds that evidence works as evidence only if there is a causal connection between evidence and hypothesis.

The second approach holds that evidence works as evidence when experience shows a regular connection (to some degree or frequency) between evidence and hypothesis.

The third approach holds that matters which work as evidence function as signs of matters (hypotheses) beyond themselves.

The third approach, to be respectable, must be stripped of the turgid nonsense in which "semiotics" has been wrapped by many literary theorists.

Much of the theorizing about evidence in the American legal academy buys into the notion that evidence works as evidence only because of experienced or observed regularities in the occurrence of distinct events or phenomena -- that evidence works as evidence only because of the relative frequencies of distinct events or phenomena. But the law in practice is generally indifferent to the relative plausibility of these three seemingly-divergent accounts of evidence, inference, relevance, and probative value; viz., the law in practice accepts much evidence whose causal connection to hypotheses of interest is not demonstrated or demonstrable; it accepts some evidence whose probative force rests on a causal account rather than on observed association or for any other apparent reason; and judges administering the law of evidence accept much evidence as worthy of consideration even when neither a causal account nor observed regularities seem to provide any apparent reason for doing so.

It is good that the law of evidence does accept any one of these three theories as orthodox and authoritative dogma. There are large grains of truth in all three accounts.

The real question, presently unanswerable, is which account best accommodates all three types of sources of human empirical knowledge.

I suspect that the best foundation for a comprehensive account of evidence and inference is laid by semiotic theory, the approach that emphasizes that evidence is an event or state that indicates or suggests a matter apart from, in addition to, or beyond itself.

The view of evidence as essentially sign, or hint, is most readily compatible with the hypothesis that both the human brain (along with its appurtenances) and the cosmos happen to be wired in such a way that a human actor has the ability to see a glimmer of a new truth based upon one encounter with some event or state of affairs -- based, in other words, on an encounter with a unique event, a singularity. And only semiotic theory explains how evidence manages to prod the human imagination to attack complex problems in quite fruitful ways, in situations that are so complex, that have so many ingredients, that random conceptual walks even over aeons of time could not be expected to yield plausible conjectures.

I will explain the above points in much more detail later -- in my promised book. Stay tuned!

Probability, the Law of Evidence, and History

Legal scholars of the law of evidence need not have inferiority complexes:

The law of evidence is the central thread in the history of probability. (James Franklin, The Science of Conjecture: Evidence and Probability before Pascal 1 (Johns Hopkins University Press, 2001)).

But, of course, legal scholars are not renowned for their modesty, yes?

The Mathematics (or Logic) of Evidence in Law: What Is It For?

Mathematical analyses of evidence take a variety of forms and can serve a variety of purposes. Hence, one cannot identify just a single possible valid legal application of mathematical analyses of evidence. But if one wishes to gain some insight into factual, or evidential, inference (and to devise procedures to facilitate inference from evidence) in and for legal proceedings, of what use (if any) is mathematics?

Some people seem to think that legal researchers who fiddle with matters such as Bayes' Theorem are attempting to construct algorithms or some such things that describe how factual inference in trials or other legal proceedings works. It is possible that this is the aim of some legal researchers, but this is generally not what I am after when I try my hand at mathematical analysis of evidence: when I fiddle with Bayes' Theorem, fuzzy logic, or whatnot, I am not attempting to depict how the institution or practice of factual proof in legal proceedings such as trials actually works. I am trying to understand inference, but this is not the same thing as trying to describe how the legal system manages evidential inference.

What might a mathematical (or logical) theory of evidence in or for legal proceedings do? If one's aim in studying the mathematics of evidence is not to describe the legal management of evidence in law, why study the mathematics of evidence (and inference)?

I have asked myself this question before. I now ask the question again because it may be particularly important if one suspects that fuzzy logic says something interesting and important about factual inference in law. A fair question is, "What possible good would a fuzzy explanation of factual proof in law do?"

One answer (one that I have sometimes also given) is that a mathematical account of inference is a valuable heuristic procedure: it is a procedure that reveals to us the implications of our own (logical?) thinking.

This answer has some force, at least sometimes. It has particular force when the heuristic procedure conforms to our untutored intuitions about the workings of sound inference: the answer -- it's all about heuristics, stupid! -- has force, for example, if we already believe that our good thinking takes a Bayesian form and a mathematical account -- in this instance, a Bayesian account -- spells out for us clearly what we roughly but imperfectly already think. This kind of use of mathematics takes us, so to speak, where we already want to go. But this heuristic justification for mathematical analysis of evidence and inference sometimes runs into trouble ...

First, there are those pesky people who refuse to concede that the basic structure of their sound thinking is Bayesian. Well, let's put those silly people to one side for now. But there are other problems ...

Second, sometimes the mathematical calculations seem to run on, so to speak, by themselves -- to such an extent that even a person who thinks that the right logical procedure is being used might feel compelled to say, "I can't honestly say that those calculations represent what I think. I think the conclusion is correct -- I have to say this because I think the method of argument used here was correct and the premises, I think, were correct -- but I can't honestly say that the calculations here portray what I already, if only faintly, thought."

The difficulty with fuzzy logic may be related to this second difficulty: the procedure does not merely elucidate what is already in someone's head. Even if one can do the calculations and personally does the calculations, the procedures and calculations do not seem to be the calculator's. So in what sense (if any) is the mathematical (or logical) procedure "heuristic"?

The law is reluctant to allow legal reasoners -- e.g., jurors, judges -- to surrender their reasoning processes to other agents or mechanisms. The law permits this to happen sometimes, but not often. This is probably one reason why the law is particularly uneasy about analytical procedures that outrun the intuitions of its authorized reasoners.

But there may be a deeper reason why the law is uneasy about -- or uninterested in -- fuzzy logic. The law may take the view that (i) certain things -- e.g., ancillary generalizations, evidential hypotheses, warrants -- must be part of any good reasoning from evidence to possible facts and (ii) fuzzy logic does not make a place, at least not in any obvious way, for such essential features of evidential inference.

"So what?," a logician might say. You are confusing logic and psycho-logic, the logician might say. For example, the logician might add, contentiously, "Just because the law has the deluded notion that ancillary generalizations -- those things you call "evidential hypotheses" -- are necessary to sound argument and inference doesn't make it so. The job of logic is not to make the human psyche comfortable.The inestimable job of logic is to devise procedures that lead to correct answers!"

It has often been noted that people have a tendency to believe the things that please them and to disbelieve matters that make them unhappy. Is it so with law as well? Does the law like to think that its logic is a good logic because thinking so makes the law and lawyers comfortable with what they do and the (deluded) way they think? Is the apparent demand of law, lawyers, and (some) legal theorists that outsiders give lawyers a transparent logic attributable to this?

Another possible answer, of course, is that the intuitions of legal folk have been right all along and that good logic must have the characteristics that legal people have thought all along that good argument must have, and logicians only now (from a longer perspective) are beginning to appreciate this. Hence, on this view, the development of theories of argumentation, the elaboration of Toulmin's theory of argument and logic, and the like are welcome and long overdue developments and are the direction that future studies of the mathematics and logic of evidence in law should take.

But this kind of justification for mathematical or logical analysis of evidence and inference seems to leave fuzzy logic out in the cold. I am not yet prepared to do that. Question: Is there not a place for a mathematical account of evidence and inference that, even though not transparent (even mildly so) to most legal professionals, sheds light on some key features of legal argument, evidential inference, and human knowledge in general? For example, even if the mathematics of fuzzy logic escapes most of us -- and will continue to escape most of us -- is it possible that it is worth studying (but why?) because it grapples with a central(?) feature of at least some legal problems -- matters such as "partial existence"? And is it possible that even if fuzzy logic and its offshoots could and would never be used by professional protagonists in courtrooms, it might nevertheless say something very important about, e.g., factual inference and the way that forensic proof ought to be conducted or managed.(We have our theories about the behavior of plants and we think that some of those theories are correct even though most of us think that the plants themselves do not have in their heads -- do plants have heads? -- the theories that we think describe how they grow etc. Perhaps legal actors such as trial lawyers are sometimes the equivalent of headless vegetables.)

Probability and Precision; Forms of Probability and Uncertainty

Probabilities are not necessarily precise. For example, we can say, "The probability of rain is between one-quarter and one-third." See generally International Society for Imprecise Probability Theory and Applications

Probabilities do not necessarily designate variability or indeterminacy in nature. Probabilities may instead represent ignorance. The former type of uncertainty may be called aleatory. (It goes by other names -- for example, chance.) The latter type of probability -- the one that represents degrees and forms of ignorance -- is often called epistemic probability or uncertainty. (This type of probability is also called different things. For example, it is sometimes called credal probability.) See Brian Weatherson, Keynes, Uncertainty and Interest Rates

The source or cause of uncertainty is important. It is important to know if our uncertainty about an event or hypothesis is attributable to the way the world works, to the chance elements in the world in which we live; or whether our uncertainty is attributable to the lack of information or our uncertainty about methods of assessing the information or evidence we have.

I have often fumbled (largely by remaining silent) in explaining the difference between my interest and the focus of people who are mainly interested in matters such as random variables and causality. The difference is that the people who are interested in the latter are generally interested in patterns of random or chance behavior in nature whereas I am more interested in incomplete evidence and inconclusive argument.

The confusion between aleatory and epistemic probability or uncertainty is perhaps partly attributable to the fact that the aleatory properties of nature often shed light on the appropriate treatment of incomplete information and on appropriate argument from and about evidence and information. In addition, it is very often the case that we have uncertainty compounded, that (some amount of) chance is wrapped in (some degree of) ignorance.

Fuzzy (Legal) Thinking -- or Precise Thinking about Fuzzy (Legal) Matters

Google "fuzzy sets" and you get 129,000 hits.

Google "fuzzy logic" and you get 600,000 hits.

Hey, jurisprudes and legal theorists! Do you think there may be a there there?

Why the general (albeit not universal) silence about fuzzy logic in the legal academy?

Don't lawyers believe in the importance of precise thinking about fuzzy and rough concepts? So why aren't they attracted (generally speaking) to a serious attempt to talk precisely about ambiguity, fuzziness, roughness, and such things? Is it because they see a basic flaw in the theoretical foundations of fuzzy logic? (This I truly doubt! They haven't gotten close enough to the theory to even begin to think about foundational issues.) Is it just because they can't get an intuitive handle on fuzzy sets, fuzzy probabilities, fuzzy measures of uncertainty, and all that? (Perhaps.) Is it because they think probability theory does a better job of describing the properties of imprecise language and imprecise concepts? (This I also doubt.)

Zadeh's more advanced work edges toward a [nominalist(?); semantic(?)] neo-Platonic [or, perhaps better described, "neo-Aristotelian"] notion of partial existence. Do legal theorists shy away from Zadeh because they cannot get a handle on the notion of a thing having some of the properties of some concept to some degree? I doubt this too!

Whether legitimately or not, legal professionals think this way all the time. What did American lawyers do when confronted with institutions that are not quite banks but are very much like banks? They called such hybrid institutions "non-bank banks." Talk about putting aside the principle of non-contradiction! Talk about partiality of existence! Talk about penumbral concepts!

Oops! This last item snuck in here via con law -- Griswold, J. Douglas, privacy, and all that. But there is an affinity here, no?

To get back to the heart of the matter: What's the story here? Fear of fuzziness, is it?

The Japanese will probably have to lead the way -- again.

Local News: Plaintiff Fraud

Headline in Sunday Star-Ledger p. 31 (County News, October 31, 2004):

State fraud files suit against carpeting chain

The Importance(?) of Understanding the Mechanics and Logic of Perception

Law journals devote quite a bit of attention to studies of the reliability and unreliability of eyewitness identification. But could the legal process produce better assessments of eyewitness reports if trial lawyers and judges knew more about the technology, or physiology, of perception and the logic that informs such perception?

Caveat: It does not necessarily follow that human knowledge of perception is presently good enough to be used in the courtroom -- and, even if such knowledge is useful "in principle" for forensic purposes, it does not necessarily follow that lawyers, judges, and jurors have the training or intelligence to make effective use of contemporary knowledge of human perception.

Counter-caveat: It is not prudent to underestimate the intellectual prowess of jurors; and some lawyers and judges have a pleasing degree of scientific literacy.

The question I pose here is not trivial -- for it is an iteration of the question of the extent to which human beings understand their world without understanding it, viz., of the extent to which human beings are capable of drawing inferences about the world without understanding the mechanics that make it work as does. Conversely stated, the question posed here implicates the question whether knowledge of causes improves inference even if it is true that some inference is possible without (much) knowledge of causes.

Counterpoint: The hypothesis that perception (truly) is (pretty good) inference suggests that human beings -- by virtue of their heredity, physiology, etc. -- know much more than they can put in words.

But the question remains: Can explicit knowledge of causes improve inference?

The answer to this question would seem to have to be "yes": It is very hard to deny that some explicitly-formulated knowledge of nature's mechanics -- e.g., gravity -- enables human beings to make better inferences and predictions (predictions are merely a special form of inference) in some situations.

A final word of caution: Even a worm knows how to burrow into the soil. (Indeed, a worm probably knows how to do that better than you do.) But (as far as I know) worms have not produced treatises on soil mechanics.

Perception as Inference (again)

E.T. Jaynes, PROBABILITY OF THEORY: THE LOGIC OF SCIENCE Section 5.4 at 133 (2003):

Seeing is not a direct apprehension of reality, as we often like to pretend. Quite the contrary: seeing is inference from incomplete information, no different in nature from the inference that we are studying here. The information that reaches us through our eyes is grossly inadequate to determine what is "really there" before us.

N.B. The discussion here does not suggest that Jaynes was intimately familiar with recent research on the logic of perception. But he was prescient in suggesting that researchers should investigate whether Bayesian logic informs perception.

Support for the Proposition that Values Depend on (Perceptions of) Facts

Some years ago I argued that there is evidence in law, that the values embedded in law (even in legislation) are in part a function of beliefs about factual propositions, including factual inferences that rest on evidence. See P. Tillers, The Value of Evidence in Law, 39 Northern Ireland Law Quarterly 167 (1988). Perhaps the following statement by Jaynes (amusing footnote omitted) offers some support for my view:

We consider it an important aspect of "objectivity" in inference -- almost a principle of morality -- that we should not allow our opinions to be swayed by our desires; what we believe should be independent of what we want. But the converse need not be true; on introspection, we would probably agree that what we want depends very much on what we know, and we do not feel guilty of any inconsistency or irrationality on that account.

E.T. Jaynes, PROBABILITY OF THEORY: THE LOGIC OF SCIENCE Section 13.12.5 at 424 (2003).

Inference Is Better-Grounded than Choice; and Analysis of Evidence Is More Secure than Economic Analysis -- Is It So?

E.T. Haynes, PROBABILITY OF THEORY: THE LOGIC OF SCIENCE Section 13.12.4 at 424 (2003):

[I]t now appears that from a fundamental standpoint loss functions are less firmly grounded than are prior probabilities. This is just the opposite of the view that propelled the Wald-inspired development of decision theory in the 1950s, when priors [prior probabilities] were regarded as vague and ill-defined, but nobody seemed to notice that loss functions are far more so. For reasons we cannot explain, loss functions appeared to workers at that time to be "real" and definite, although no principles for determining them were ever given, beyond the truism that any function with a continuous derivative appears linear if we examine a sufficiently small piece of it.

In the meantime, there have been several advances in the technique for assigning priors by logical analysis of prior information. But, to the best of our knowledge, we have as yet no formal principles at all for assigning numerical values to loss functions; not even when the criterion is purely economic, because the utility function of money remains ill-defined.

Great Law Schools & Great Libraries

My law school does not do badly in the law school ratings game. But the law school rating services play a poor game because they generally ignore one crucial measure of the greatness of a law school: the quality of a law school's library.

We can have endless debates about whether a law school either is ought to be essentially an academic institution or a professional school, or whether the academic-professional divide is a false one. But -- regardless position we take on such issues -- all sensible law teachers and legal practitioners should agree on one point: much of law centers on TEXT. Hence, a great law school, regardless of how it defines its mission, must be a great repository of textual material (cases, treatises, journals, the lot).

If a law school is to grant text its proper role in the life of a law school, the law library must be a sanctuary, and the library ought to be an inviting and alluring sanctuary. For example, the seats should be comfortable and the physical environment should be aesthetically pleasing and warm. The library must be so arranged that its "customers" want to spend time in it.

A great law school must have a great library. Does US News & World Report know this? Does Brian Leiter know this?

Apparently not.

N.B. My law school fares worse -- not better -- if "library quality" is a measure of the quality of a law school. So this post does not serve a narrowly-conceived personal interest.

A Stellar Conjunction -- or a (non)Lunatic One

Will the Red Sox win the World Series just at the moment that the moon goes blank? If so, are the Red Sox responsible? Or is the moon responsible? Which way does the chain of causation run? Is non-Luna pulling the Red Sox or are the Red Sox eclipsing the moon? I need a Latin phrase here. ("Post hoc, propter hoc"?)

European Morality

"Hussein's government killed an estimated 300,000 people, most of them Shi'ite Muslims or ethnic Kurds, rights groups say. The Iraqi government has identified about 40 mass graves, but until now none has been scientifically exhumed -- in part because European forensic teams won't collect evidence that might be used to win death penalty convictions." Thanassis Cambanis, "In Iraq grave, evidence of regime's horrors," Boston Globe (online) (October 13, 2004).

What Is "What Is Evidence?"?

Some scholarly discussions of the law of evidence begin with a question such as "What is evidence?" or "What is proof?" See, e.g., I Wigmore on Evidence Section 1 (P. Tillers rev., 1983).

Questions such as these have a mind-numbing quality; they have a tendency to paralyze thought.

Why? Is there a better way to consider the nature of matters such as "evidence" and "proof"?

Perhaps questions of the form "What is ... [some thing or phenomenon in law]?" induce mental or intellectual paralysis in part because such questions incline the observer to launch a search for attributes which, when properly assembled and arranged, could constitute -- the observer may hope -- a correct or adequate definition of a phenomenon such as "evidence" or "proof." If a non-solipsistic observer conducts a non-circular search for the attributes of a (complex[!]) social(?!) phenomenon such as "legal evidence," (s)he is likely to generate a very long list of attributes. Such a list of features may end up being a mere aggregation of attributes that resembles a serving of thick porridge unaccompanied by any explanation for the identity or quantity of the ingredients found therein.

I do not wish to overstate my objection to starting discussion of the law of evidence with a definition: it is unlikely that conceptual mush is an inevitable effect of launching an investigation with a request or search for a definition. I only wish to suggest that acquiring an understanding of the nature of a legal phenomenon or practice such as the law of evidence is not best promoted by formulating and then pondering assertions such as "legal proof is an epistemic process," "judicial proof is a legal process" and "judicial proof is a symbolic process," and that the search for an understanding of a matter such as legal proof is better promoted by formulating topics of discussion in the following fashion: "scarcity in proof," "time in proof," "evidence in legal proof," "argument in legal proof," and so on.

A restatement of the general question under discussion in this post:

Is it fair -- or is it instructive -- to begin a discussion of the law of evidence or proof with a definition or definitions of matters such as "evidence" or "proof"?

A tentative answer to the (reformulated) general question:

A question such as "What is [legal] evidence?" is in part an empirical question: unless one is a Platonist -- or unless one denies the possibility of social variation --, a good answer to such a question always requires in part an account of what is conventionally considered to be a thing such as evidence.

True, a definition of phenomenon such as "evidence" or "proof" should not be a mere catalogue of the matters that are considered "evidence" or "proof": a good definition crystallizes a wide diversity of phenomena; a good definition resembles a rule that generates or explains (perhaps only by and large) a wide and diverse collection of phenomena that might be considered instances of a matter such as "legal evidence." But it does not follow that one ought to begin a scholarly discussion of a legal field such as the law of evidence with a rule or formula that (putatively) specifies the essential or important attributes of a matter such as "evidence" or "proof." It is probably better instead to proceed quasi-empirically and quasi-inductively: judgments about the important or "essential" attributes of matters such as "legal evidence" should emerge out of ruminations based on our observations of the real-world workings of matters such as "the law of evidence" or "proof in legal proceedings." (Such ruminations may, but need not, devolve into bare quasi-statistical statements of the relative frequency of various attributes in a process such as "proof in legal proceedings.")

N.B. Is it not the case that for some purposes -- including the present one -- a good "definition" of a social phenomenon and practice such as "judicial proof" must include an account of the motivation(s) for the phenomenon or practice? (Construe "motivation(s)" broadly: make it encompass "function(s).")

Postscript #1: Definitions -- properly and broadly understood -- are important. One needs them to understand the spirit of a social phenomenon or practice that, because of its variety and diversity, may otherwise seem bereft of rhyme or reason.

Postscript #2:The ruminations in this post are intended only for (actual or aspiring) authors of legal texts. (These ruminations are, in any event, unlikely to interest anyone else.)

Sir Richard on Sir Arthur

Judge Richard Posner finds little to admire in Sherlock Holmes' methods. See R. Posner, "CSI: Baker Street," New Republic (October 11, 2004 [which is, BTW, surely a fictitious publication date {since I am reasonably sure that today is October 4, 2004, and in my limited human experience the clock and the calendar do not run backwards, but who am I to say they could not?} -- explain this, ye besotted publishers of journals a/k/a ye purveyors of 21st century versions of Soviet-style histories]).

Judge Posner thinks some or many of Holmes' deductions are little more than a shot in the dark -- and are therefore unscientific.

Verily, verily, I say unto ye ("thee"?; i.e., "to all of you out there"): science requires shots in the dark, shots that are merely(!) prompted, or suggested, by evidence.

Verily, verily, I say unto thee: science depends on careful deductions but it also depends on abductions a/k/a imaginative hypotheses suggested but not dictated by evidence or logic.

Verily, verily I say unto thee -- or ye, or y'all: imaginative reasoning is not an oxymoron -- and, besides, where would we be without Einstein's imagination, an imagination par excellence but an imagination that could work its wiles only because of Einstein's meticulous attention to details and matters such as clocks and their synchronization in distant places [for train schedules and other such purposes]? {You surely don't expect me to answer this last question, do you? The best answer I can give you now: not quite where we are now.}

Take Two Samples ...

Take two samples of handwriting, practically any two samples. Make sure the two samples are made by different people. Question: If you look close enough and long enough, how probable is it that you will find the same extraordinarily rare combination of characteristics in the two samples?

Many years ago I followed exactly this procedure. I had a group of students write down the same phrase twice on two different pieces of paper and then throw their handwriting samples into a hat. I then picked two samples that I knew -- or believed -- had been written by two different people. (I think I asked the students to write their names on the back of each piece of paper with their handwriting samples on the front and I had the students do this before they knew what I was up to.) As I said just moments ago, I picked, more or less at random, two handwriting samples that had been made by different people, by different students. I then scrutinized these two handwriting samples for a while. After doing so, I found about a dozen handwriting quirks that occurred in both samples. I pointed out these similarities to the class. I then did some product rule calculations and I asked the class to do the same with the probability values (and dependencies) that they thought were appropriate. I then asked the students in the class whether they thought the two samples were written by the same person. Everyone (in a class of ca. 25) answered in the affirmative. (I had somehow managed to instruct the actual authors of the two samples to keep their mouths shut.) When I told the students that in fact two different students had produced the handwriting samples, about five students found my confession to be both astonishing and unbelievable; and despite my confession of trickery, they argued that the two sample had been written by the same person.

As I recall, statements by the two students who (I think) actually made the two samples overcame the objections of the dissenting students.

I believe I successfully tricked the class. But I can't really say that the dissenters were completely befuddled or irrational, can I?

Dreyfus redux?

My pedagogical trick would not have worked if one writer had written English and the other, Arabic. It would not have worked if one author had been 25 years old and the other, three years old. Therefore?

Improbable DNA

Jennifer Mnookin, "Fingerprint Evidence in an Age of DNA Profiling," 67 Brooklyn L. Rev. 13, 49-50 (2001)(footnotes omitted):

[I]n a 1999 case in England ... Raymond Easton was charged with burglary after authorities made a "cold hit" with his DNA in a DNA database. His DNA matched the crime scene DNA at six loci. Because there was only a one in thirty-seven million chance that a randomly selected person's DNA would match, Raymond Easton was charged with burgling a house 200 miles from where he lived. However, after Easton, who had advanced Parkinson's disease and was unable even to drive a car, offered an alibi for the night in question, the DNA was eventually tested at four more loci. This more sophisticated test showed there was no DNA match after all. All charges were dropped.

Investigating Multiple SIDs Deaths

Question for the day:

If the number of multiple SIDS ("sudden infant death syndrome") deaths within single families within some large population is exactly what one would expect if chance alone governs the distribution of SIDS, should government authorities investigate for possible wrongdoing if the only thing they know is that there were, apparently, three SIDS deaths within a single family?

Further questions:

(i) Are three such deaths within a single family ever sufficient for a criminal conviction of a person who alone had access to the children when they died?

(ii) If not, would four deaths suffice?

(iii) If not, would five or ... n deaths ever suffice?

Dice, Probability, and Law

There is more to probability than dice and games of chance. Nonetheless, I think it is probably(!?) useful to use dice to introduce law students to some basic points about probability theory. I like to use a set of large "fair" dice. (Later I will perhaps post a [true!] story about my unsuccessful attempt to buy magnetized dice.) This Monday I will also try to use the nifty applet at the following web site to make several points: Introduction to Probability Models.

Magnetized dice would be a nice way to illustrate dependent probabilities.

Repeated rolls of dice (with, e.g., the applet mentioned above) can be used, I think, to show, by analogy, some of the problems that can arise with the use of statistics about the relative (in)frequency of SIDS to prove criminal guilt or, even, with the use of such statistics to justify "just" coercive investigation by the state.

A Timely Closing Argument

In a baby murder trial in which the baby finally died of suffocation, the prosecutor -- Michael D'Andrea -- "asked the jury to look at the clock while one minute ticked by -- the amount of time it would have taken [the baby] to suffocate. As the time elapsed, D'Andrea stared directly into [defendant's] face from across the defense table." Michaelangelo Conte, "Jury takes just three hours to convict mother's boyfriend in baby's death," The Jersey Journal pp. A1 & A10 (September 22, 2004).

I saw some fancy lawyering when I practiced law in Texas (many years ago). But New Jersey lawyers, it seems, have their own bags of tricks.

Some Gentle Readers out there can surely relate stories about similar forensic tricks they have seen; I doubt that Mr. D'Andrea is the first trial lawyer to ask a jury to literally watch a clock for 60 seconds or so. In civil litigation the best-known parallel, now generally frowned upon, is for plaintiff's counsel in a personal injury case to ask a jury to imagine how much suffering plaintiff must endure each second of his or her life, put a dollar value on each second's suffering, and then tote up all of those dollars and return a handsome verdict for plaintiff.