Electoral systems and the distortion of voters' preferences

Piolatto, Amedeo (2008): Electoral systems and the distortion of voters' preferences.

Abstract

In this paper I show that in a parliamentary democracy, contrary to common wisdom, under a proportional electoral rule governments do not necessarily represent voters' preferences better than under plurality rule. While voters affect the composition of Parliament, decisions are taken by a subset of Parliamentarians: a coalition of them decides directly and through the government. As a consequence, two distortions might occur: one at the electoral stage when Parliament is formed and the other at the coalition formation stage, when government is chosen. Through a model à la Rubinstein, I show that small parties' bargaining power increases when parties are patient; for sufficiently patient parties, the small (but pivotal) ones obtain a large bargaining power. The distortion introduced by plurality rule goes in the opposite direction; this can be beneficial (in term of voters' representativeness) as long as the impact of the two distortions is similar. I show that under non restrictive conditions, plurality rule can outperform the proportional rule in terms of representativeness of voters' preferences.

• Item Type: MPRA Paper
• Language: English
• Keywords: Electoral systems; Proportional rule; Plurality rule; Voters' representation
• Subjects: H - Public Economics > H1 - Structure and Scope of Government; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D72 - Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior; P - Economic Systems > P1 - Capitalist Systems > P16 - Political Economy

References

Amer, R., F. Carreras, and J. M. Gimenez (2002). The modified Banzhaf value for games with coalition structure: an axiomatic characterization. Mathematical Social Sciences 43, p. 45-54.

Auriol, E. and R. J. Gary-Bobo (2008). On the optimal number of representatives. IDEI Working Paper, n. 86.

Austen-Smith, D. and J. Banks (1988). Elections, coalitions, and legislative outcomes. The American Political Science Review 82, 405-422.

Austen-Smith, D. and J. S. Banks (1990). Stable governments and the allocations of portfolios. American Political Science Review 84, 891-906.

Axelrod, R. (1970). Conflict of interest: a theory of divergent goals with applications to politics. Markham.

Bandyopadhyay, S. and M. Oak (2008). Coalition governments in a model of parliamentary democracy. European Journal of Political Economy 24, 554-561.

Banks, J. and J. Duggan (2000). A bargaining model of collective choice. American Political Science Review 94, 73-88.

Baron, D. and D. Diermeier (2001). Elections, governments, and parliaments in proportional representation systems. The Quarterly Journal of Economics 116, 933-967.

Baron, D., D. Diermeier, and P. Fong (2007). A dynamic theory of a parliamentary democracy, Research Paper Series No.1960, Stanford Business School.

Baron, D. P. (1989). A noncooperative theory of legislative coalitions. The American Journal of Political Science 33, 1048-1084.

Baron, D. P. (1993). Government formation and endogenous parties. American Political Science Review 87, 34-47.

Baron, D. P. and J. A. Ferejohn (1989). Bargaining in legislatures. The American Political Science Review 83(4), 1181-1206.

Blau, A. (2001). British Elections and Parties Review, vol. 11, Chapter 4: Partisan bias in British general elections, pp. 46-65. Frank Cass.

de Swaan, A. (1973). Coalition Theories and Government Formation. Elsevier.

Diermeier, D., H. Eraslan, and A. Merlo (2007). Bicameralism and government formation. Quarterly Journal of Political Science 2, 227-252.

Diermeier, D. and A. Merlo (2004, March). An empirical investigation of coalitional bargaining procedures. Journal of Public Economics 88(3-4), 783-797.

Diermeier, D. and P. v. Roozendaal (1998). The duration of cabinet formation processes in western multi-party democracies. British Journal of Political Science 28(4), 609-626.

Douglas, P. H. (1923). The necessity for proportional representation. International Journal of Ethics 34(1), 6-26.

Duverger, M. (1954). Political Parties. New York, Wiley.

Gamson, W. (1961). A theory of coalition formation. American Sociological Review 26, 373-382.

Hooghe, M., B. Maddens, and J. Noppe (2006). Why parties adapt: electoral reform, party finance and party strategy in Belgium. Electoral studies 25, 351-368.

Kalandrakis, T. (2006). Proposal rights and political power. American Journal of Political Science 50, 441-448.

Kestelman, P. (1999). Quantifying representativity. Voting matters 10.

Laakso, M. and R. Taagepera (1981). Proportional representation and effective number of parties in Finland. In M. Holler (Ed.), Power, Voting and Voting Power, pp. 107-120. Physica-Verlag, Wurzburg.

Laver, M. and K. Shepsle (1990). Coalition and cabinet government. American Political Science Review 84, 873-890.

Leiserson, M. (1968). Factions and coalitions in one-party Japan: an interpretation based on the theory of games. American Political Science Review 62, 70-87.

Marichal, J.-L., I. Kojadinovic, and K. Fujimoto (2007). Axiomatic characterizations of generalized values. Discrete Appl. Math. 155(1), 26-43.

Martin, L. W. and R. T. Stevenson (2001). Government formation in parliamentary democracies. American Journal of Political Science 45(1), 33-50.

Morelli, M. (2004). Party formation and policy outcomes under different electoral systems. Review of Economic Studies 71, 829-853.

Nurmi, H. (1981). The problem of the right distribution of the voting power. In M. Holler (Ed.), Power, Voting and Voting Power, pp. 203-212. Physica-Verlag, Wurzburg.

Owen, G. (1977). Values of games with a priori unions. In R. Henn and O. Moeschlin (Eds.), Essays in Mathematical Economics and Game Theory, pp. 76-88. Springer-Verlag.

Owen, G. (1981). Modification of the Banzhaf-Coleman index for games with a priori unions. In M. Holler (Ed.), Power, Voting and Voting Power, pp. 232-238. Physica-Verlag, Wurzburg.

Qualter, T. (1968). Seats and votes: an application of the cube law to the Canadian electoral system. Canadian Journal of Political Science 1, 336-344.

Riker, W. H. (1962). The theory of political coalitions. Yale University press.

Riker, W. H. (1982). The two-party system and Duverger's law: an essay on the history of political science. American Political Science Review 76, 753-766.

Rogowski, R. and M. A. Kayser (2002). Majoritarian electoral systems and consumer power: price-level evidence from the OECD countries. American Journal of Political Science 46, 526-539.

Rubinstein, A. (1982). Perfect equilibrium in a bargaining model. Econometrica 50, 97-109.

Schofield, N. (1981). The relationship between voting and party strength in an electoral system. In M. Holler (Ed.), Power, Voting and Voting Power, pp. 121-134. Physica-Verlag, Wurzburg.

Schofield, N. (1986). Existence of a 'structurally stable' equilibrium for a non-collegial voting rule. Public Choice 51, 267-284.

Sened, I. (1996). A Model of Coalition Formation: Theory and Evidence. The Journal of Politics 58, 350-372.

Shapley, L. S. (1953). A value for n-person games. In H. Kuhn and A. Tucker (Eds.), Contributions to the Theory of Games II, pp. 307-317. Princeton Univ. Press.

Snyder Jr., J. M., M. M. Ting, and S. Ansolabehere (2005). Legislative bargaining under weighted voting. American Economic Review 95(4), 981-1004.

Taagepera, R. and M. S. Shugart (1989). Seats and votes: the effects and determinants of electoral systems. Yale University Press.

van den Brink, R. and G. van der Laan (2005). A class of consistent share functions for games in coalition structure. Games and Economic Behavior 51, 193-212.

Wiese, H. (2007). Measuring the power of parties within government coalitions. International Game Theory Review 9, 307-322.