(Page 3 of 30) - A Model of Adversarial Committees authored by Kim, Jaehoon.

classical Condorcet Jury Theorem considers a model in which every juror has homogenous
preferences but diﬀers in the probability of making a correct decision. The main result is
that under majority rule, the probability of a correct decision by the jury is higher than
that of any individual, and the probability of a correct decision goes to one as the size of
the jury becomes very large. However, Austen-Smith and Banks (1995) demonstrate that
if individuals start from a common prior about guilt of the defendant and then obtain
private information, it is generally not a Nash equilibrium to vote sincerely. Subsequent
works by Wit (1998) and McLennan (1998) show that the main arguments of the Theorem
are robust even if individuals vote strategically according to a symmetric mixed strategy
equilibrium of the game.

Feddersen and Pesendorfer (1998) compute a juror’s symmetric responsive strategy ex-

plicitly and demonstrate that equilibrium voting behavior is sensitive to the voting rule. In
large juries, the probability of convicting the innocent defendant is larger under the una-
nimity rule than under non-unanimity rules. Gerardi (2000) shows that when each juror
has uncertainty about other jurors’ preferences, the unanimity rule can protect innocent
defendants against mistaken convictions. Duggan and Martinelli (2001) and Meirowitz
(2002) consider the case in which the signals are drawn from a continuous distribution;
the former conﬁrms Feddersen and Pesendorfer (1998)’s results for the continuous signal
model, but the latter shows that the collective makes the correct decision almost surely
as population size grows under any voting rule, in particular, unanimity rule.

Not surprisingly we ﬁnd that the unanimity rule in an adversarial committee results in

a gridlock, meaning that an adversarial committee almost always decides on the status
quo against the alternative proposal when the size of the committee goes to inﬁnity. Even
when an alternative proposal is chosen, it is not majority-preferred with a probability close
to 1/2. Thus, group decision-making under the unanimity rule is equivalent to individual
decision-making without any private information, implying that the unanimity rule fails
to aggregate information. Hence, collective decision-making under the unanimity rule is
almost always inferior to individual decision-making based on private information.

Under non-unanimous rules, we assume that majority-type voters are sensitive to the

possibility of making a wrong choice given that they are not perfectly informed. Then
an adversarial committee with a large size almost always chooses a majority-preferred
alternative if the proportion of the majority-type voters is greater than the fraction of the
required votes to pass the alternative. Otherwise, an adversarial committee almost always
chooses the status quo as in the unanimity rule. Thus, such a non-unanimous rule fails to
aggregate information.

As a consequence of relation between the proportion of majority-type and the fraction

of the required votes under a given non-unanimous rule, only simple majority rule is
minority-dominance proof. Under non-unanimous rules except for simple majority rule,
in a large committee there exists a possibility of minority-dominance when majority-type
voters ignore their private information and vote for the alternative in equilibrium.