Abstract
This paper investigates the impact of a supermajority rule on the law of 1/n, which posits that a larger number of districts increases the size of government. Our analysis suggests that supermajority rule, despite the claim that it restrains excessive spending, increases the 1/n effect, because qualified majorities require logrolling to attract additional members. Using data from US states from 1970 to 2007, we find that the adoption of a supermajority rule has a robust, worsening effect on the fiscal commons problem identified by the law of 1/n.
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Notes
As legislature size increases, vote trading becomes more important to pass a spending project, leading to the approval of more projects.
The proposal for a spending project exceeding the threshold must be approved by majority of voters in a referendum.
This paper does not address the aggregation of demand within a district because supermajority rules are associated with formulation of the coalition across districts.
More general cases (\(0\,<\,\gamma\,<\,1\)) give qualitatively similar results.
The closed rule prevents amendments once a proposal has been made.
Stationarity means that each legislator takes the same action in structurally identical subgames (Baron and Ferejohn 1989; Primo 2006). A member’s continuation value equals his expected payoff in any round. Note that a more inclusive voting rule (i.e., an increase in m) reduces the size of agenda setter’s projects, thus limiting the tendency for the agenda setter to exploit other coalition members.
Note that \(z (p V) = \underset{z}{{\text {{argmax}}}} [u(z) - m \cdot (p/n) \cdot z]\), where \(u(\cdot )\) is the value of z to coalition members. In the standard formulation of the law of 1/n, \(z (p/n) = \underset{z}{{{\text {argmax}}}} [u(z) - (p/n) \cdot z]\).
More generally, E can be written as \(p \cdot m^{\gamma } \cdot z (p V)\), which implies that \(E_n = \gamma \cdot p \cdot n^{\gamma - 1} \cdot V^{\gamma } \cdot z (p V)\).
If \(\gamma = 0\), E can be written as \(p \cdot z (p V)\), from which \(E_n = 0\) given V.
Primo (2006) finding is partially driven by the assumption that costs of projects are convex.
The issue of multicollinearity involving \(S_{it}\) and \(N_{it}\) is ignored because the correlations between the two variables are low (−0.08 for lower chambers and −0.18 for upper chambers).
Only Nebraska has a unicameral structure.
Supermajority states typically adopted the rules in 10-year waves.
Total revenue is treated the same as expenditure because most American states have balanced budget requirements and cannot expect a bailout from the federal government (McKinnon and Nechyba 1997). Note that many state governments finance capital spending (e.g., schools and highways) by issuing bonds, and that only the interest payments on those bonds appear in the public budget.
Dropping the population variable did not affect the results.
The marginal effects are based on the estimation results in (5) and (6).
Data refer to the average values for the 1970–2007 period.
Calculation is based on the results in column (7).
Regression outputs used to calculate the marginal effects are available upon request to the author.
This intuition is based on Ansolabehere et al. (2003).
Legislators in the upper house are assumed to choose the outcome most preferred by the median voter of their constituency. We also assume that lower-house districts with equal population are completely nested within the upper-house districts. Note that in some states, boundaries of districts in the upper house and lower house cross each other.
Unequal chamber sizes in the presence of supermajority rules would add to the interest group’s problem of allocating campaign contributions and lobbying effort across the two chambers optimally.
A member’s continuation value C equals his expected payoff in any round: \((m-1)/n \times C + 1/n \times (E - (m-1)C) + (n-m)/n \times 0\). Thus, \(C = E/n\), and the agenda setter keeps \(E - (m-1) \cdot E/n\).
One way to think about this is that the agenda setter receives side payments from other coalition members—i.e., the difference between project values and continuation values.
Note that the net benefits for a legislator in district i are \(u(z_{i}) - (z_{1} + z_{2} + ... + z_{m}) \cdot p/n\). Summing this across all m coalition members gives U. By standard assumption, u is concave and increasing in \(z_{i}\).
Thus the agenda setter effectively allocates projects of size \(pV \cdot z(pV)\) to exactly \(m-1\) other coalition members, and allocates a project of size \(pV \cdot z(pV) \cdot (n - m + 1)\) to herself.
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Acknowledgments
I wish to thank an anonymous reviewer, editors William F. Shughart II and Pete Leeson, Thomas E. Borcherding, and Sangwon Park for valuable insight and suggestions. This paper was supported by Faculty Research Fund, Sungkyunkwan University, 2013.
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Appendix
Appendix
In equilibrium, the agenda setter offers \(m-1\) coalition members their continuation values—i.e., E/n per member—and keeps the remaining value for herself—i.e., \(E \cdot (n-m+1)/n\).Footnote 27 In every period, the \(m-1\) members who receive an offer of E/n vote for the proposal, and all other members vote against it. The agenda setter votes for the proposal because \(E \cdot (n-m+1)/n \ge E/n\).
The bargaining outcome indicates that the agenda setter selects m district projects of total value E that will maximize her payoff. Note that the agenda setter keeps the bargaining surplus through side payments, effectively sharing in the projects of other coalition members.Footnote 28 The agenda setter thus selects district projects as if to maximize the sum of the utilities of all coalition members. Intuitively, the agenda setter maximizes the size of the pie to be divided among the coalition members. This means selecting a set of projects \((z_{1}, z_{2},...,z_{m})\) to maximize:
where \(u(z_{i})\) is the value of \(z_{i}\) to the ith coalition member.Footnote 29 The first-order conditions are \(u^{\prime } (z_{i}) = p \cdot (m/n), \forall i \in (1,...,m)\). Noting that \(p \cdot (m/n) \equiv p V\), the first-order conditions imply that \(z_{i}^{*} = z(pV)\) for all i. Since each of m legislators gets z(pV), the total government expenditures E can be written as \(p \cdot m \cdot z (p V)\).Footnote 30
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Lee, D. Supermajority rule and the law of 1/n . Public Choice 164, 251–274 (2015). https://doi.org/10.1007/s11127-015-0271-x
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DOI: https://doi.org/10.1007/s11127-015-0271-x