The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to StatisticsVenn, John
Philosophy
The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to Statistics
Venn, John
Chance; Logic, Symbolic and mathematical; Probabilities; Science -- Methodology
The first of these would aim at determining the standard
of judicial certainty indirectly, by simply determining the
statistical frequency with which the decisions (say) of a jury
were found to be correct. This may seem to be a hopeless
task; and so indeed it is, but not so much on any theoretic
insufficiency of the determining elements as on account of
the numerous arbitrary assumptions which attach to most
of the problems which deal with the probability of testimony
and judgments. It is not necessary for this purpose that we
should have an infallible superior court which revised the
decisions of the one under consideration;[26] it is sufficient if a
large number of ordinary representative cases are submitted
to a court consisting even of exactly similar materials to the
one whose decisions we wish to test. Provided always that we
make the monstrous assumption that the judgments of men
about matters which deeply affect them are 'independent'
in the sense in which the tosses of pence are independent,
then the statistics of mere agreement and disagreement will
serve our purpose. We might be able to say, for instance,
that a jury of a given number, deciding by a given majority,
were right nine times out of ten in their verdict. Conclusions
of this kind, in reference to the French courts, are
what Poisson has attempted at the end of his great work on
the Probability of Judgments; though I do not suppose that
he attached much numerical accuracy to his results.
A scarcely more hopeful means would be found by a
reference to certain cases of legal 'presumptions.' A 'conclusive
presumption' is defined as follows:--"Conclusive, or
as they are elsewhere termed imperative or absolute presumptions
of law, are rules determining the quantity of evidence
requisite for the support of any particular averment
which is not permitted to be overcome by any proof that the
fact is otherwise."[27] A large number of such presumptions
will be found described in the text-books, but they seem to
refer to matters far too vague, for the most part, to admit of
any reduction to statistical frequency of occurrence. It is
indeed maintained by some authorities that any assignment
of degree of Probability is not their present object, but that
they are simply meant to exclude the troublesome delays
that would ensue if everything were considered open to
doubt and question. Moreover, even if they did assign a
degree of certainty this would rather be an indication of
what legislators or judges thought reasonable than of what
was so considered by the juries themselves.
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