State 0
State 1
Status Quo
Alternative
Alternative
Group
0
−1
1
Table 1
Payoff Matrix under Common Objective
have focused on how strategic actions influence predictions regarding the collective decision
realized.
Another important aspect of the Condorcet Jury Theorem, however, has received less
attention; that the Condorcet Jury Theorem implicitly assumes that every member of
a collective decision-making body has a common objective. While a reasonable assump-
tion in a jury setting, in many interesting political decision-making circumstances this
homogeneity of objective is quite restrictive given conflicting interests.
To illustrate what the commonality of objective means in group decision-making, con-
sider the payoff matrix in Table 1. Here every group member wants to have the status quo
in state 0 and the alternative in state 1. Clearly, this assumption is problematic for leg-
islative decision-making in a multi-party system, a prominent feature of such institutions
is party competition. Legislative party politics is usually portrayed as a zero-sum game,
with one party’s gain of a seat equalizing on other parties’ loss. Even if parties agree on a
long-term national objective, they may disagree on specific issues for many reasons. One
such reason is their electoral concerns. We argue that such concerns create heterogeneous
objectives and conflicting preferences.
Such opposing state-contingent preferences are illustrated in Table 2, in which members
of group 1 prefer the status quo rather than the alternative in state 0, while it is the
opposite for members of group 2, and vice versa in state 1. In many political situations,
we believe that such preferences are prevalent. As such, the homogeneity assumption
of individual preferences may restrict the applicability of the Condorcet Jury Theorem
and associated results in the literature. We call an adversarial committee a committee
composed of voters with opposing state-contingent preferences. In this paper we explore
the performance of different voting rules in an adversarial committee. We find information
aggregation results that starkly contrast those previously found.
Let us briefly summarize the previous literature on the Condorcet Jury Theorem. The
State 0
State 1
Status Quo
Alternative
Alternative
Group 1
0
−1
1
Group 2
0
1
−1
Table 2
Payoff Matrix under Heterogeneous Objectives
2
Convention