_CONCERNING THE PROBABILITY OF THE JUDGMENTS OF TRIBUNALS._
Analysis confirms what simple common sense teaches us, namely, the
correctness of judgments is as much more probable as the judges are more
numerous and more enlightened. It is important then that tribunals of
appeal should fulfil these two conditions. The tribunals of the first
instance standing in closer relation to those amenable offer to the
higher tribunal the advantage of a first judgment already probable, and
with which the latter often agree, be it in compromising or in desisting
from their claims. But if the uncertainty of the matter in litigation
and its importance determine a litigant to have recourse to the tribunal
of appeals, he ought to find in a greater probability of obtaining an
equitable judgment greater security for his fortune and the compensation
for the trouble and expense which a new procedure entails. It is this
which had no place in the institution of the reciprocal appeal of the
tribunals of the district, an institution thereby very prejudicial to
the interest of the citizens. It would be perhaps proper and conformable
to the calculus of probabilities to demand a majority of at least two
votes in a tribunal of appeal in order to invalidate the sentence of the
lower tribunal. One would obtain this result if the tribunal of appeal
being composed of an even number of judges the sentence should stand in
the case of the equality of votes.
I shall consider particularly the judgments in criminal matters.
In order to condemn an accused it is necessary without doubt that the
judges should have the strongest proofs of his offence. But a moral
proof is never more than a probability; and experience has only too
clearly shown the errors of which criminal judgments, even those which
appear to be the most just, are still susceptible. The impossibility of
amending these errors is the strongest argument of the philosophers who
have wished to proscribe the penalty of death. We should then be obliged
to abstain from judging if it were necessary for us to await
mathematical evidence. But the judgment is required by the danger which
would result from the impunity of the crime. This judgment reduces
itself, if I am not mistaken, to the solution of the following question:
Has the proof of the offence of the accused the high degree of
probability necessary so that the citizens would have less reason to
doubt the errors of the tribunals, if he is innocent and condemned, than
they would have to fear his new crimes and those of the unfortunate ones
who would be emboldened by the example of his impunity if he were guilty
and acquitted? The solution of this question depends upon several
elements very difficult to ascertain. Such is the eminence of danger
which would threaten society if the criminal accused should remain
unpunished. Sometimes this danger is so great that the magistrate sees
himself constrained to waive forms wisely established for the protection
of innocence. But that which renders almost always this question
insoluble is the impossibility of appreciating exactly the probability
of the offence and of fixing that which is necessary for the
condemnation of the accused. Each judge in this respect is forced to
rely upon his own judgment. He forms his opinion by comparing the divers
testimonies and the circumstances by which the offence is accompanied,
to the results of his reflections and his experiences, and in this
respect a long habitude of interrogating and judging accused persons
gives great advantage in ascertaining the truth in the midst of indices
often contradictory.
The preceding question depends again upon the care taken in the
investigation of the offence; for one demands naturally much stronger
proofs for imposing the death penalty than for inflicting a detention of
some months. It is a reason for proportioning the care to the offence,
great care taken with an unimportant case inevitably clearing many
guilty ones. A law which gives to the judges power of moderating the
care in the case of attenuating circumstances is then conformable at the
same time to principles of humanity towards the culprit, and to the
interest of society. The product of the probability of the offence by
its gravity being the measure of the danger to which the acquittal of
the accused can expose society, one would think that the care taken
ought to depend upon this probability. This is done indirectly in the
tribunals where one retains for some time the accused against whom there
are very strong proofs, but insufficient to condemn him; in the hope of
acquiring new light one does not place him immediately in the midst of
his fellow citizens, who would not see him again without great alarm.
But the arbitrariness of this measure and the abuse which one can make
of it have caused its rejection in the countries where one attaches the
greatest price to individual liberty.
Now what is the probability that the decision of a tribunal which can
condemn only by a given majority will be just, that is to say, conform
to the true solution of the question proposed above? This important
problem well solved will give the means of comparing among themselves
the different tribunals. The majority of a single vote in a numerous
tribunal indicates that the affair in question is very doubtful; the
condemnation of the accused would be then contrary to the principles of
humanity, protectors of innocence. The unanimity of the judges would
give very strong probability of a just decision; but in abstaining from
it too many guilty ones would be acquitted. It is necessary, then,
either to limit the number of judges, if one wishes that they should be
unanimous, or increase the majority necessary for a condemnation, when
the tribunal becomes more numerous. I shall attempt to apply calculus to
this subject, being persuaded that it is always the best guide when one
bases it upon the data which common sense suggests to us.
The probability that the opinion of each judge is just enters as the
principal element into this calculation. If in a tribunal of a thousand
and one judges, five hundred and one are of one opinion, and five
hundred are of the contrary opinion, it is apparent that the probability
of the opinion of each judge surpasses very little ½; for supposing it
obviously very large a single vote of difference would be an improbable
event. But if the judges are unanimous, this indicates in the proofs
that degree of strength which entails conviction; the probability of the
opinion of each judge is then very near unity or certainty, provided
that the passions or the ordinary prejudices do not affect at the same
time all the judges. Outside of these cases the ratio of the votes for
or against the accused ought alone to determine this probability. I
suppose thus that it can vary from ½ to unity, but that it cannot be
below ½. If that were not the case the decision of the tribunal would be
as insignificant as chance; it has value only in so far as the opinion
of the judge has a greater tendency to truth than to error. It is thus
by the ratio of the numbers of votes favorable, and contrary to the
accused, that I determine the probability of this opinion.
These data suffice to ascertain the general expression of the
probability that the decision of a tribunal judging by a known majority
is just. In the tribunals where of eight judges five votes would be
necessary for the condemnation of an accused, the probability of the
error to be feared in the justice of the decision would surpass ¼. If
the tribunal should be reduced to six members who are able to condemn
only by a plurality of four votes, the probability of the error to be
feared would be below ¼. There would be then for the accused an
advantage in this reduction of the tribunal. In both cases the majority
required is the same and is equal to two. Thus the majority remaining
constant, the probability of error increases with the number of judges;
this is general whatever may be the majority required, provided that it
remains the same. Taking, then, for the rule the arithmetical ratio, the
accused finds himself in a position less and less advantageous in the
measure that the tribunal becomes more numerous. One might believe that
in a tribunal where one might demand a majority of twelve votes,
whatever the number of the judges was, the votes of the minority,
neutralizing an equal number of votes of the majority, the twelve
remaining votes would represent the unanimity of a jury of twelve
members, required in England for the condemnation of an accused; but one
would be greatly mistaken. Common sense shows that there is a difference
between the decision of a tribunal of two hundred and twelve judges, of
which one hundred and twelve condemn the accused, while one hundred
acquit him, and that of a tribunal of twelve judges unanimous for
condemnation. In the first case the hundred votes favorable to the
accused warrant in thinking that the proofs are far from attaining the
degree of strength which entails conviction; in the second case, the
unanimity of the judges leads to the belief that they have attained this
degree. But simple common sense does not suffice at all to appreciate
the extreme difference of the probability of error in the two cases. It
is necessary then to recur to calculus, and one finds nearly one fifth
for the probability of error in the first case, and only 1/8192 for this
probability in the second case, a probability which is not one
thousandth of the first. It is a confirmation of the principle that the
arithmetical ratio is unfavorable to the accused when the number of
judges increases. On the contrary, if one takes for a rule the
geometrical ratio, the probability of the error of the decision
diminishes when the number of judges increases. For example, in the
tribunals which can condemn only by a plurality of two thirds of the
votes, the probability of the error to be feared is nearly one fourth if
the number of the judges is six; it is below 1/7 if this number is
increased to twelve. Thus one ought to be governed neither by the
arithmetical ratio nor by the geometrical ratio if one wishes that the
probability of error should never be above nor below a given fraction.
But what fraction ought to be determined upon? It is here that the
arbitrariness begins and the tribunals offer in this regard the greatest
variety. In the special tribunals where five of the eight votes suffice
for the condemnation of the accused, the probability of the error to be
feared in regard to justice of the judgment is 65/256, or more than ¼.
The magnitude of this fraction is dreadful; but that which ought to
reassure us a little is the consideration that most frequently the judge
who acquits an accused does not regard him as innocent; he pronounces
solely that it is not attained by proofs sufficient for condemnation.
One is especially reassured by the pity which nature has placed in the
heart of man and which disposes the mind to see only with reluctance a
culprit in the accused submitted to his judgment. This sentiment, more
active in those who have not the habitude of criminal judgments,
compensates for the inconveniences attached to the inexperience of the
jurors. In a jury of twelve members, if the plurality demanded for the
condemnation is eight of twelve votes, the probability of the error to
be feared 1093/8192, or a little more than one eighth, it is almost 1/22
if this plurality consists of nine votes. In the case of unanimity the
probability of the error to be feared is 1/8192, that is to say, more
than a thousand times less than in our juries. This supposes that the
unanimity results only from proofs favorable or contrary to the accused;
but motives that are entirely strange, ought oftentimes to concur in
producing it, when it is imposed upon the jury as a necessary condition
of its judgment. Then its decisions depending upon the temperament, the
character, the habits of the jurors, and the circumstances in which they
are placed, they are sometimes contrary to the decisions which the
majority of the jury would have made if they had listened only to the
proofs; this seems to me to be a great fault of this manner of judging.
The probability of the decision is too feeble in our juries, and I think
that in order to give a sufficient guarantee to innocence, one ought to
demand at least a plurality of nine votes in twelve.