affinities, but we do not model these explicitly. For a merger to take place, both
merging groups must agree; if not, they form separate parties.5
The outcome of this stage is a party system, where parties are indexed by P. If
a party represents only one economic group, J, we index this party P = J. If two
groups of legislators merge, the resulting party represents two economic groups, I
and J ; and we write the party index as P = IJ. Three outcomes are thus possible:
a two-party system, (P =12and P = 34), a four-party system (P =1, 2, 3, 4),
and a three-party system (P =12, 3, 4, or P =1, 2, 34). We let N denote the
equilibrium number of parties, and the possible outcomes by N = II, III, IV .
Let NWP denote the expected payoff of party P, at the start of the next
(government-formation) stage of the game, i.e., its continuation utility after party
formation, once N parties have formed. These payoffs are described more precisely
below, except for the following natural assumptions: if political group J remains
a party on its own, its expected continuation payoff coincides with that of the
group-specific party: NWJ = NWP , with P = J. If instead political groups I and
J merge, each one expects to receive one half of the expected continuation payoff
of the merged party N W J = 2 N W P, with P = IJ.
A four-party system is an equilibrium if — taking into account the expected
equilibrium outcome of subsequent stages — the groups of legislators representing
economic groups I and J find it optimal to remain split, given that the other
two groups have also decided to stay split, i.e., IV W P > 2 III W IJ, for P = I, J.
This condition must hold for I and J =1, 2 or 3, 4. Equilibrium conditions for a
two-party, or a three-party, system are formulated in an analogous way.6
2.2.2. Government formation
After party formation, but before any policy decisions, a government is formed.
We keep this stage of the game as simple as possible, skipping any strategic
interactions, by just postulating an exogenous stochastic process for government
formation. Any government needs the support of at least half the legislature.
In line with our assumptions about party formation, we only allow governing
5 This assumption only matters when we introduce asymmetries: if the model is symmetric,
the incentives to merge or remain split are the same for the pair contempleting a merger.
6 The assumption of four primitive groups in the legislature is not restrictive. We could
instead have assumed the initial legislature to consist of two or three parties, allowing them to
splinter into smaller group-specific parties. Nothing of substance would change in this alternative
formulation and the same set of equilibrium party systems would result with suitable changes
in notation.