But the incentive turns the other way if the opposition is united. Note that this
result is directly related to the first past the post character of the electoral rule
and should be robust to other representations of heterogeneity.
Result (ii) is more directly related to the specific modeling assumptions. When
parties 1 and 2 merge, we are back to the homogeneity case with the groups
represented in the coalition representing half of the electorate in each district.
This result should not be robust to different representations of heterogeneity.
Result (iii) says that total rents are higher under heterogeneity cum coalition
governments. This is because, contrary to the case of homogeneity, parties in
government mainly compete with the opposition rather than with each other about
electoral seats.
The results on equilibrium party formation are expressed in:.
Proposition 6
Under the above assumptions on heterogeneity:
(i) A two-party equilibrium exists only if 1++γ S^) ≤ 2-+β + 3 ;
(ii) A three-party equilibrium with P =1, 2 remaining split and P =3, 4
merging always exists if (42+β) — 2(2-'β) ≥ 6.
The appendix gives the analysis. When β increases, the condition for a 2-party
equilibrium becomes more stringent. The main and intuitive insight is that the
two parties, P =1, 2, with a ”home advantage” in concentrated districts have
less incentives to merge than under homogeneity, because the electoral benefits
from doing so are smaller. The main benefit from merging is that reward votes
to the coalition partner not well represented in a district are not ”lost ” but
accrue to the merged party. This is not a huge advantage. On the other hand,
the cost of sharing power in a merged party remains the same. Therefore, one
is less likely to see a two party equilibrium and might see instead a three party
equilibrium, as stated in part (ii) of Proposition 6. Note also that the conditions
for a three-party equilibrium become more easy to fulfill as heterogeneity goes up
(β increases).
The result in Proposition 6 leads to the empirical prediction that two party
equilibria and single-party governments are less likely to be observed under ma-
joritarian rule if electoral districts are sufficiently heterogeneous in the distribution
of voters. As a corollary, coalition governments should be more frequent, which
in turn could lead to a larger government spending. Of course, this prediction
may be difficult to take to the data since district heterogeneity is very hard to
measure for a large sample of countries. Note that, by Proposition 5, if districts
are heterogeneous the electoral rule might exert a direct effect on the overall size
31