The Gazette 1983

NOVEMBER 1983

GAZETTE

and Rules of Proof

Probability Theory

by John O'Connor M.Sc.(Mngt.), C.Eng.,

F.I.Struct.E., F.IEI., M.Cons.E.I.*

T O the uninformed the concepts of a case being proved "beyond a reasonable doubt" or "on the balance of probabilities" is not at all specific. True, both statements indicate a standard of proof less than certainty itself, and we shall begin by adopting the commonsense definitions of Denning L.J. in Miller -v- Minister of Pensions '. In a criminal case the evidence "need not reach certainty, but it must carry a high degree of pr obab i l i t y . . .. (it) does not mean proof beyond the shadow of a doubt". The balance of probabilities was defined as when the Court can say "we think it more probable than not . . . . but if the probabilities are equal the burden is not discharged". 2 It follows from these definitions that certainty is not required and it is important to note the use of the word "probabilities" in both definitions. In essence, therefore, the burden of proof is discharged by a standard of probability which depends on whether the case is criminal or civil. Certainty, being the ultimate level of probability is of course acceptable, but not necessary to establish guilt or liability. The word 'probability' is subjective and its meaning will vary with the circumstances of its use. In Walker -v- Dept. of Trade and Industry 1 the Court had to decide on the meaning of "the probable amount of the cash balance". These words appear in Section 89(2) of the English Bankruptcy Act 1914. It was held that the words "probable amounts" referred to small amounts only and not to large amounts. It follows that there is no intrinsic legal meaning of the word 'probable' and all definitions rest on a subjective assessment of the circumstances of its use. It is obvious that this use of the word "probable" is part of the language of law and not of science. In science, one may find two further meanings of "probability" contained within the disciplines of pure mathematics and statistics. A. J. Ayer 4 has given the following meanings to "probability" as outlined above. (a) 'A priori' probability or the mathematical calcula- tion of chances per abstract games of chance. (b) Statistical probability which introduces the notion of "limiting frequency". In essence it is simply the experiment being carried out so often that further experiment will not affect the result by more than a small amount. (c) Finally, the legal use of the word "probability", which Mr. Ayer is pleased to call "a statement of credibility". The larger question is whether the scientific definitions of probability are useful in directly establishing burden of proof, i.e., is it possible by using a pure mathematical

formula for chance events, or by the use of statistical evidence to prove guilt or liability? The answer is no. Although technical evidence on the chances of events occurring as deduced by pure maths have a place in the courtroom, that place is limited. The reasons lie in the origin of scientific and legal terminology. They are not compatible and the same word can have a different meaning in legal affairs and affairs of science. For instance, the word 'law' to the lawyer represents an intangible idea of an authority demonstrated by Bracton in the thirteenth century. He said "That the King should not be under man, but under God and the Law". 5 Lord Denning in fact claimed that Bracton "was the first to make the law into a science" 6 , but he was mistaken. Science is precise, rigorous and impersonal while the law is impossible to measure or predict. Again, a scientific 'law' is inferior in ranking to a scientific 'theory'. The essential element in science is certainty and argument and opinion bows to scientific measurement. It is possible to trace the development of a theory which illustrates the absence of subjective judgement and demonstrates that the certainty required by science is not possible to satisfy in a courtroom, except in the limited case of expert scientific evidence. The development of a scientific theory is indicated later diagramatically. This begins with a collection of facts, which is a very low form of scientific research. Scienti- fically, these facts are then used to develop Concepts, e.g., the fact that man exists leading to the concept of man as a father, worker or law student, etc. These concepts give rise to the Hypothesis which is where the legal system and the scientific system separate. At this level, the law has already run its course. The collection of facts and the analysis of the concept of the litigants as plaintiff/defendant complete the legal exercise. In science the analysis of concepts is just a further step leading to a hypothesis to be postulated and tested in the manner "if A is done then B will probably occur". For instance, if a load is attached to a strand of wire, then the wire will extend. Is this always true? The answer is yes and we arrive at the scientific definition of a law which is that whenever a phenomenon occurs consistently in any part of the globe with similar experimental results then that hypothesis has achieved the status of a law. In our case, the extension of the strand of wire is related to applied load up to certain limits and gives rise to Hookes law or the law that stress is proportional to strain. Since stress is load per unit area and strain is defined as extension of strand under load divided by original length we can write: 249