# A Test of the Marginalist Defense of the Rational Voter Hypothesis Using Quantile Regression

## Abstract

This chapter uses quantile regression to uncover variations in the strength of the relationship between the expected closeness of the outcome, size of the electorate and voter turnout in Norwegian school language referendums. Referendums with a low turnout show a weak positive effect of closeness and a strong negative effect of size, the opposite being true of referendums with a high turnout. The results substantiate the marginalist defense of the Downsian rational voter hypothesis, which asserts that, while closeness and size cannot explain the absolute level of turnout, they can account for change at the margin.

## Keywords

Rational voter theory Voter turnout Quantile regression## Notes

### Acknowledgments

I would like to thank Morten Søberg, who provided the data on Norwegian school language referendums, and Dennis C. Mueller for constructive criticism.

## References

- Aldrich, J. H. (1995).
*Why parties? The origin and transformation of political parties in America*. Chicago: University of Chicago Press.CrossRefGoogle Scholar - Aldrich, J. H. (1997). When is it rational to vote? In D. C. Mueller (Ed.),
*Perspectives on public choice*(pp. 373–390). Cambridge: Cambridge University Press.Google Scholar - Barry, B. (1970).
*Sociologists, economists, and democracy*. London: Collier Macmillan Publishers.Google Scholar - Blais, A. (2000).
*To vote or not to vote: The merits and limits of rational choice theory*. Pittsburgh: University of Pittsburgh Press.Google Scholar - Brennan, H. G., & Hamlin, A. (2000).
*Democratic devices and desires*. Cambridge: Cambridge University Press.Google Scholar - Brennan, H. G., & Lomasky, L. E. (1997).
*Democracy and decision*. Cambridge: Cambridge University Press.Google Scholar - Chamberlain, G., & Rothschild, M. (1981). A note on the probability of casting a decisive vote.
*Journal of Economic Theory*,*25*, 152–162.CrossRefGoogle Scholar - Costa, D. L., & Kahn, M. E. (2003). Civic engagement and community heterogeneity: An economist’s perspective.
*Perspectives on Politics**1*, 103–111. Unpublished manuscript, Harvard University.Google Scholar - Downs, A. (1957).
*An economic theory of democracy*. New York: Harper & Row.Google Scholar - Edlin, A., Gelman, A., & Kaplan, N. (2005).
*Voting as a rational choice: The effect of preferences regarding the well-being of others*. Unpublished manuscript, University of California, Berkeley.Google Scholar - Feddersen, T., & Pesendorfer, W. (1996). The swing voters curse.
*American Political Science Review*,*86*, 408–424.Google Scholar - Good, I., & Mayer, L. (1975). Estimating the efficacy of a vote.
*Behavioral Science*,*20*, 25–33.CrossRefGoogle Scholar - Grofman, B. (1981). Fair apportionment and the Banzhaf index.
*The American Mathematical Monthly*,*88*, 1–5.CrossRefGoogle Scholar - Grofman, B. (1993). Is turnout the paradox that ate rational choice theory? In B. Grofman (Ed.),
*Perspectives on public choice*(pp. 93–103). University of Michigan Press.Google Scholar - Kaniovski, S. (2008). The exact bias of the Banzhaf measure of power when votes are neither equiprobable nor independent.
*Social Choice and Welfare*,*31*, 281–300.CrossRefGoogle Scholar - Kaniovski, S., & Mueller, D. C. (2006). Community size, heterogeneity and voter turnouts.
*Public Choice*,*129*, 399–415.CrossRefGoogle Scholar - Kirchgässner, G., & Schimmelpfennig, J. (1992). Closeness counts if it matters for electoral victory: Some empirical results for the United Kingdom and the Federal Republic of Germany.
*Public Choice*,*73*, 283–299.CrossRefGoogle Scholar - Kirchgässner, G., & Schulz, T. (2005).
*Expected closeness or mobilisation: Why do voters go to the polls?—empirical results for Switzerland, 1981–1999*. Unpublished manuscript, University of St.Gallen.Google Scholar - Koenker, R. (2005).
*Quantile regression*. New York: Econometric Society Monographs, Cambridge University Press.Google Scholar - Koenker, R., & Bassett, G. W. (1978). Regression quantiles.
*Econometrica*,*46*, 30–50.CrossRefGoogle Scholar - Koenker, R., & Hallock, K. F. (2001). Quantile regression.
*Journal of Economic Perspectives*,*15*, 143–156.CrossRefGoogle Scholar - Matsusaka, J. G., & Palda, F. (1993). The Downsian voter meets the ecological fallacy.
*Public Choice*,*77*, 855–878.CrossRefGoogle Scholar - Mueller, D. C. (2003).
*Public choice III*. Cambridge: Cambridge University Press.Google Scholar - Riker, W. H., & Ordeshook, P. C. (1968). A theory of the calculus of voting.
*American Political Science Review*,*62*, 25–42.CrossRefGoogle Scholar - Schachar, R., & Nalebuff, B. (1999). Follow the leader: Theory and evidence on political participation.
*American Economic Review*,*89*, 525–549.CrossRefGoogle Scholar - Schuessler, A. A. (2000).
*A logic of expressive choice*. Princeton: Princeton University Press.Google Scholar - Søberg, M., & Tangerås, T. P. (2004).
*Rational voter turnout*. Evidence from 232 Norwegian referendums. Unpublished manuscript, The Research Institute of Industrial Economics, Stockholm.Google Scholar - Tullock, G. (1967).
*Towards a mathematics of politics*. Ann Arbor: University of Michigan Press.Google Scholar