whether their individual utility is above or below a given reservation utility level.
Ideology nevertheless plays a role in that they reward or punish the party repre-
senting their group differently than parties representing other groups. Specifically,
citizen i in group J votes for party J when it is in government if:
VJ(q) ≥ ωi + δ + VJ . (2.6)
If the inequality turns the other way, she votes for the opposition; if the opposi-
tion has more than one party, each opposition party receives her vote with equal
probability. If party J is not in government and if inequality (2.6) is satisfied,
then in case there is a government coalition, each party in the coalition receives
her vote with equal probability; if the inequality is not satisfied, she votes for her
“own” party. Voters thus reward their own party more often than other parties10.
The first term on the right hand side of (2.6) depicts an individual component
of reservation utility: ωi is uniformly distributed within each group of voters,
with mean zero and density φ. Individuals with higher values of ωi are more
demanding of the incumbent government. The second term is a random shock to
the popularity of the incumbent government, common to all voters. We assume
that δ is also uniformly distributed, with mean 0 and density ψ. Thus, we can
think of φ as a measure of within-group voter mobility, and ψ as a measure of
aggregate mobility between government and opposition (higher values correspond
to higher mobility). The last term is given by V*J = VJ(qG), where qG denotes the
equilibrium policy vector, for a given party structure, a given type of government
and a given electoral rule — as shown below, the number of parties in the legislature
has no influence on equilibrium policy once we control for the type of government.
It reflects the voters’ expectations of what the government can reasonably be
expected to deliver, given the political circumstances in which policy is set.
As we will see, these assumptions imply that in equilibrium on average half
of the voters vote for the incumbent government while the remaining half votes
for the opposition. When the incumbent government sets policy, it knows the
distributions for ωi and δ, but not the realization of the aggregate popularity
shock δ. As in other probabilistic voting models, this uncertainty creates a smooth
mapping from policy to expected vote shares.
10As we will see below, this behavioral assumption is important because it induces a conflict
among parties in a coalition government. It creates an electoral incentive for a political party P
in government to please the group it represents, but not the group represented by the coalition
partner.
10