Under majoritarian elections, a four-party system is always an equilibrium.
But for some parameter values, a two-party system is also an equilibrium out-
come. The two-party equilibrium is more likely to exist under the conditions enu-
merated in Proposition 3, that also make rents higher under proportional than
majoritarian elections.
Before turning to the case of heterogeneity, let us try and summarize the empir-
ical implications of the four numbered propositions above. According to Propo-
sitions 2 and 4, the equilibrium number of parties and hence the incidence of
coalition governments can be smaller under majoritarian elections, particularly
under the conditions listed in Proposition 3 (ii). According to Proposition
3 (i), overall government spending is always larger under coalition governments
than under single-party governments, and the electoral rule affects spending only
via its effect on the incidence of coalition governments. When it comes to rent
extraction, the electoral rule has an independent effect, but the sign is ambiguous.
By Propositions 3 and 4, however, the smallest rents are likely to be observed
in those majoritarian democracies where two-party systems and single-party gov-
ernments are most often observed.
At a general level, these predictions rhyme well with the general idea in the
political-science literature, that proportional elections go hand in hand with “rep-
resentativeness” and majoritarian elections go hand in hand with “accountability”.
But the predictions are sharper than general insights, and give quite clear guid-
ance on how we may want to take the model’s implications for party structures,
types of government, and economic policies to the data.
5. Heterogeneity
Heterogeneity in the distribution of voters across districts can be represented in
many ways. This section presents a simple model, which illustrates that equilibria
under majoritarian elections can be quite different when electoral districts are
heterogenous.
As before, we assume that groups J =3, 4 are homogeneously distributed
across districts and, each, constitute one fourth of the electorate. But group
J = 1 now has 1+4β of the votes in half of the districts, d ∈ [0,1 ] and 1-β of the
votes in the other half while the distribution for group J =2 is the mirror image
of this. Parameter β ∈ [0, 1] represents the degree of geographical concentration
of groups J =1and 2.Whenβ =0, we have the prior homogeneity case, and
when β = 1, we have maximum heterogeneity: groups J = 1 and 2 each represent
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