L.J. COHEN, THE PROBABLE AND THE PROVABLE

pp. 77-81 (1977)

THE DIFFICULTY ABOUT NEGATION

Consider, for example, a case in which it is common ground that 499 people paid for admission to a rodeo, and that 1,000 are counted on the seats, of whom A is one. Suppose no tickets were issued and there can be no testimony as to whether A paid for admission or climbed over the fence. So by any plausible criterion of mathematical probability there is a .501 probability, on the admitted facts, that he did not pay. The mathematicist theory would apparently imply that in such circumstances the rodeo organizers are entitled to judgement against A for the admission-money, since the balance of probability (and also the difference between prior and posterior probabilities) would lie in their favour. But it seems manifestly unjust that A should lose his case when there is an agreed mathematical probability of as high as .499 that he in fact paid for admission.

Indeed, if the organizers were really entitled to judgement against A, they would presumably be equally entitled to judgement against each person in the same situation as A. So they might conceivably be entitled to recover 1,000 admission-moneys, when it was admitted that 499 had actually been paid. The absurd injustice of this suffices to show that there is something wrong somewhere. But where?...

An important part of the trouble seems to be that, if standards of proof are interpreted in accordance with a theory of probability that has a complementational principle for negation, the litigants are construed as seeking to divide a determinate quantity of case-merit, as it were, between them. Such an interpretation treats it as an officially accepted necessity that the merit of the loser's case in a civil suit varies inversely with that of the winner's, and this generates paradox where proof is allowed on the mere balance of the two probabilities. Nor can we say thenas lawyers sometimes do say in practicethat the defendant's case is equally good on the facts in both of two similar lawsuits, while the plaintiff's case is better in one than the other. But we can say this quite consistently, and avoid the paradox, if we abandon any complementational principle for negation. We may then suppose litigants to be taking part in a contest of case-strength or case-weight, rather than dividing a determinate quantity of case-merit. The only possibility of injustice that is then officially countenanced is the possibility that one side may not have put forward as strong a case as it could. But where that happens it is the fault of the litigant or of his lawyers or witnesses, not of the legal system.... [I]f standards of juridical proof are interpreted in terms of inductive, rather than mathematical, probabilities this is precisely what follows.

The point under discussion has not gone unnoticed in the courts. A Massachusetts judge once remarked

It has been held not enough that mathematically the chances somewhat favour a proposition to be proved; for example, the fact that coloured automobiles made in the current year outnumber black ones would not warrant a finding that an undescribed automobile of the current year is coloured and not black.... After the evidence has been weighed, that proposition is proved by a preponderance of evidence if it is made to appear more likely or probable in the sense that actual belief in its truth, derived from the evidence, exists in the mind or minds of the tribunal notwithstanding any doubts that may still linger there.(1)

In other words the standard of proof in civil cases is to be interpreted in terms leading one to expect that, after all the evidence has been heard, a balance of probability in favour of a certain conclusion will produce belief in the truth of that conclusion among reasonable men. So we need a concept of probability that admits a threshold for rational acceptance, or moderate belief, which is quite distinct from the threshold for belief beyond reasonable doubt.

1. . Lummus, J., in ``Sargent v. Massachusetts Accident Co.,'' 307 Mass. 246, 29 N.E.2d 825, 827 (1940) quoted by V.C. Ball, ``The moment of truth: probability theory and the standards of proof,'' in Essays on Procedure and Evidence ed. T.G. Rondy Jr. and R.N. Covington (1961), p.95.


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