utility of the local public good gJ for a quarter of the population is equated to the
opportunity cost of private consumption for the whole population, namely unity.
Political rents are set at zero.
2.2. The political system
We model the political system as a multistage game. All stages take place within
the single period described in the previous subsection (we discuss below how to
extend the model to a multiperiod framework). We can think of this single period
as the life of a legislature, beginning right after the preceding election and ending
with a fixed election date. The legislature consists of four groups of legislators,
each representing one of the economic groups discussed above.
The game has four consecutive stages: a party formation stage, when the four
groups of legislators can either form group-specific parties, or merge into larger
parties; a government formation stage, when a government supported by a legisla-
tive majority is formed; a policy formation stage, when the government (and its
legislative majority) sets economic policy; an election stage, when citizens observe
their welfare and vote for one of the existing parties. The rules of the game are
always the same, except for the electoral rule: we compare equilibria under pro-
portional and majoritarian elections. Before we delve into that comparison, the
remainder of this section describes and discusses the extensive form of the game
in each of its four stages.
2.2.1. Party formation
Just after the previous elections, each political group in the legislature has a simple
choice: whether to form a separate group-specific party, or to merge into a new
and larger party with another group. At the outset, the legislature thus consists of
four political groups, numbered from 1 to 4, each representing one of the economic
groups. The precise meaning of the word “representing” is explained when we
describe the election stage, below. For simplicity, we assume that each political
group has an initial seat share of 1/4 (under suitable assumptions discussed below,
the results can be generalized to arbitrary initial seat shares).
The decision whether to merge or (remain) split is made strategically by these
groups, taking into account subsequent equilibrium outcomes. We simplify the
strategy space by only allowing mergers between groups 1 and 2, and groups
3 and 4 respectively. This restriction could be justified by invoking ideological