one half of the electorate in one half of the districts, but are not represented at all
in the other half. This parametrization has the advantage of preserving symmetry
between J =1 and 2 while creating asymmetry between the first two and the last
two groups.
Intuitively, one would expect parties 1 and 2 to have a ”home advantage ” in
their districts and therefore to have less incentives to merge, while 3 and 4 would
have a strong incentive to merge to compete successfully with parties 1 and 2 in
their districts. This raises the possibility of a three party equilibrium.
To keep this section short, we present the main results in the form of propo-
sitions and intuition for these results. The Appendix gives the details of the
underlying calculations. Since proportional elections have only a single national
district, heterogeneity cannot be an issue. Hence, we only discuss majoritarian
elections.
Proposition 5 compares the equilibrium policy under heterogeneity with the
benchmark of the previous section, where all districts are homogeneous. We fo-
cus on the policy choices of governments formed by parties J = 1, 2 when in
government, i.e., the parties with geographically concentrated representation.
Proposition 5
When geographical party concentration, as measured by β, increases:
(i) Coalition governments formed by parties representing geographically con-
centrated groups spend more on their own groups and even more so when the
opposition is split, but spend less on the groups in the opposition, and even more
so when the opposition is split;
(ii) Single-party governments formed by a party representing geographically
concentrated groups spend the same amount as single-party governments under
homogeneous districts, irrespective of the number of parties in the opposition;
(iii) Equilibrium rents are the same as under homogeneity for single-party gov-
ernment, but higher for coalition governments.
The most important result is the first one. Each coalition member has a
relatively stronger incentive to please voters from their own constituency in the
districts where these voters are overrepresented. The total effect on spending is not
clear a priori, however, because higher spending for the groups in government may
be more or less than offset by reduced spending for the groups in the opposition.
Under heterogeneity, equilibrium policy can vary with the number of parties, in
contrast to Proposition 1 and 3. Indeed, when the opposition (J =3, 4) is
divided, each opposition party receives only half of the votes of the dissatisfied
voters, which gives less incentives for the coalition parties to target those groups.
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