344 A. W. F. Edwards
for the preference obsolete. The probabilistic revolution applied the calculus of
probability, invented in connection with games of chance, to the problem of the
observational errors of astronomy and geodesy. The failure of a hypothesis to ac-
count exactly for observational data was no longer seen as a fault of either the
hypothesis or the data, but as a measurable reflection of the random component
in the observations.Anceps fortuna aequitate rationis reprimiturPascal had writ-
ten in 1654 — ‘Proper calculation masters fickle fortune’ (see [Edwards, 2002d]).
People still wanted simple hypotheses, but they were now probabilistic ones, and
needed to be judged not only by simplicity but by a definite measure of how well
they explained the data — by ‘likelihood’.
An example will make clear how probabilistic reasoning leads naturally to the
Darwin principle. Suppose we hear that a friend has borne male twins. Are they
identical? If so, the probability that they are both boys is 1/2, but if they are not
identical the probability is 1/4 (assuming that boys occur with probability 1/2).
Setting aside for the moment any question of the prior probabilities, the likelihood
ratio in favour of the twins being identical is therefore 2:1. The hypothesis of
the single origin of the male sex is better supported than the hypothesis of two
separate origins. Now suppose that the character about which we are told is not
sex but a much rarer genetic character segregating in families with low frequency
p. The twins both have this character. Are they identical?
This time the probability that they both possess the character ispif they are
identical, butp^2 if they are not. The likelihood ratio in favour of identical twins
is thereforep:p^2 or 1:p, which is large and convincing ifpis small. The more
improbable the event that has been observed, the greater the support for the
hypothesis of a single origin. The word ‘likelihood’ is here used in its technical
statistical sense defined by Fisher [1921]. A full account of it will be found in
Edwards [1972; 1992].
The Darwin principle was, of course, in use in connection with human simi-
larities millenia before Darwin. Noone ever suggested that each individual was
a special creation like a pre-Darwinian species (souls were another matter), and
inferring relationship from similarity of appearance must always have reflected a
subconscious desire to avoid having to account independently for similar facial and
other features. Darwin himself, in a rare mention of the ‘doctrine of chances’, was
more explicit [1859], unwittingly using a likelihood argument for the complemen-
tary problem of inferring inheritance given a known relationship:
When a deviation appears not unfrequently, and we see it in the father
and child, we cannot tell whether it may not be due to the same orig-
inal cause acting on both; but when amongst individuals, apparently
exposed to the same conditions, any very rare deviation, due to some
extraordinary combination of circumstances, appears in the parent —
say, once amongst several million individuals — and it reappears in
the child, the mere doctrine of chances almost compels us to attribute
its reappearance to inheritance.