The Gazette 1983

GAZETTE

NOVEMBER 1983

Probability Theory

John O'Connor

M.Sc

.(Mngt.), C.Eng.,

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".

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

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

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

and Rules of Proof

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

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".

Lord Denning in fact claimed that Bracton "was the

first to make the law into a science"

, 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:

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