As a result, it is still optimal to set the tax rate at its maximum: t = 1. With distortionary taxes, however, the lower costs of taxation would have led to a higher tax rate. The sharper incentives to redistribute also show up in the optimal supply of public goods, as the optimal tradeoff between b2 and g now fulfills:
The condition is identical to (3.7), except that d replaces sS in the expression for — d|p. Since s2 < 3s = s*, higher rents make the candidates lose votes at a higher rate in majoritarian elections. Intuitively, the electoral competition is stiffer, as it is now focused on the district with the most responsive voters. Because the election outcome is more sensitive to policy, the two parties become more disciplined and forego some prospective (endogenous) rents Source.
What happens to these comparative politics results, if we relax the extreme assumption about perfect overlap between groups and districts? Qualitatively, the answer is “nothing”, provided that the middle-class group 2 is a “dominant group” in one of the districts.12 Let the population share of group i in district k be denoted by n*,fc. Then, group 2 is a dominant group in one of the districts if n2,fc > 1 and n1,fc, n3,fc < 1 in some k. If the middle class dominates district 2, in this sense, electoral competition will take place only in district 2. Furthermore, district 2 is an asymmetric replica of the whole population, where group 2 receives more weight. As illustrated in Figure 2, this asymmetry has the same effect as a higher relative density -- of group 2 under proportional elections, the result of which was discussed in subsection 3.2; more redistribution towards group 2, less public goods, and less rents.
The central comparative politics results of this section can be succinctly summarized. Majoritarian elections make electoral competition stiffer, by concentrating it in some key marginal districts. The result is more targeted redistribution in a more narrow constituency. With majoritarian elections, we should therefore not only observe more targeted redistribution towards the politically influential middle class, but also a lower supply of public goods and smaller rents, ceteris paribus. Extending the model with distortionary taxes, we also get the prediction that majoritarian elections should be associated with larger governments.
Before turning to the evidence, however, we discuss a different model of political behavior, which focuses on institutions governing policy formation.
We now drop the unrealistic assumption that binding commitments to policy platforms can be made ahead of elections. In the real world, there is no outside authority that can enforce campaign promises. And even if there was (or if reputational incentives were strong enough), many policy-relevant states of the world are non-describable or non-verifiable. Precise state-contingent policy promises can thus not be formulated or would not be believed by the voters. This suggests that political constitutions are analogous to incomplete contracts; they allocate decision rights to different actors. Policy choices are made by incumbent politicians, once in office, so the elections select a decision maker, not a state contingent policy. In particular, voters hold politicians accountable for their performance through retrospective voting.