"A Model of Jury Decisions where All Jurors have the Same Evidence"
Franz Dietrich
Group on Philosophy, Probability and Modelling
Center for Junior Research Fellows
University of Konstanz, 78457 Konstanz
Germany
and
Christian List
Nuffield College
Oxford, OX1 1NF, England
ABSTRACT. In the classical Condorcet jury model, different jurors'
votes are independent random variables, where each juror has the
same probability p>1/2 of voting for the correct alternative. The
probability that the correct alternative will win under majority
voting converges to 1 as the number of jurors increases. Hence the
probability of an incorrect majority vote can be made arbitrarily
small, a result that may seem unrealistic. A more realistic model
is obtained by relaxing the assumption of independence and relating
the vote of every juror to the same "body of evidence". In terms of
Bayesian trees, the votes are direct descendants not of the true
state of the world ('guilty' or 'not guilty'), but of the "body of
evidence", which in turn is a direct descendant of the true state
of the world. This permits the possibility of a misleading body of
evidence. Our main theorem shows that the probability that the
correct alternative will win under majority voting converges to
the probability that the body of evidence is not misleading, which
may be strictly less than 1.
Keywords: Condorcet jury theorem, conditional independence,
interpretation of evidence, Bayesian trees
JEL classification nos: D71 and D72