Public Choice

, Volume 179, Issue 1–2, pp 97–111 | Cite as

Why Arrow’s theorem matters for political theory even if preference cycles never occur

  • Sean InghamEmail author


Riker (Liberalism against populism, Waveland, New York, 1982) famously argued that Arrow’s impossibility theorem undermined the logical foundations of “populism”, the view that in a democracy, laws and policies ought to express “the will of the people”. In response, his critics have questioned the use of Arrow’s theorem on the grounds that not all configurations of preferences are likely to occur in practice; the critics allege, in particular, that majority preference cycles, whose possibility the theorem exploits, rarely happen. In this essay, I argue that the critics’ rejoinder to Riker misses the mark even if its factual claim about preferences is correct: Arrow’s theorem and related results threaten the populist’s principle of democratic legitimacy even if majority preference cycles never occur. In this particular context, the assumption of an unrestricted domain is justified irrespective of the preferences citizens are likely to have.


Arrow’s impossibility theorem Populism Democratic legitimacy Popular will 



The author is grateful to Wulf Gaertner, Lucas Stanczyk, and David Wiens for comments on earlier drafts.


  1. Arrow, K. (1963). Social choice and individual values (2nd ed.). New Haven, CT: Yale University Press.Google Scholar
  2. Austin-Smith, D., & Banks, J. (1999). Positive political theory I: Collective preference. Ann Arbor, MI: University of Michigan Press.CrossRefGoogle Scholar
  3. Banks, J. (1995). Acyclic social choice from finite sets. Social Choice and Welfare, 12(3), 293–310.CrossRefGoogle Scholar
  4. Bellamy, R. (2007). Political constitutionalism: A republican defence of the constitutionality of democracy. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  5. Brennan, J. (2016). Against democracy. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
  6. Christiano, T. (2008). The constitution of equality: Democratic authority and its limits. Oxford: Oxford University Press.CrossRefGoogle Scholar
  7. Cohen, J. (1986). An epistemic conception of democracy. Ethics, 97(1), 26–38.CrossRefGoogle Scholar
  8. Dennett, D. C. (2013). Intuition pumps and other tools for thinking. New York, NY: W.W. Norton & Company.Google Scholar
  9. Dowding, K. (2006). Can populism be defended? William Riker, Gerry Mackie and the interpretation of democracy. Government and Opposition, 41(3), 327–346.CrossRefGoogle Scholar
  10. Dryzek, J. S., & List, C. (2003). Social choice theory and deliberative democracy: A reconciliation. British Journal of Political Science, 33, 1–28.CrossRefGoogle Scholar
  11. Elster, J. (2011). How outlandish can imaginary cases be? Journal of Applied Philosophy, 28(3), 241–258.CrossRefGoogle Scholar
  12. Knight, J., & Johnson, J. (2011). The priority of democracy: Political consequences of pragmatism. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
  13. Lippert-Rasmussen, K. (2008). Against self-ownership: There are no fact-insensitive ownership rights over one?s body. Philosophy & Public Affairs, 36(1), 86–118.CrossRefGoogle Scholar
  14. Mackie, G. (2003). Democracy defended. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  15. Morreau, M. (2010). It simply does not add up: Trouble with overall similarity. The Journal of Philosophy, 107(9), 469–490.CrossRefGoogle Scholar
  16. Müller, J.-W. (2016). What is populism?. Philadelphia, PA: University of Pennsylvania Press.CrossRefGoogle Scholar
  17. Okasha, S. (2011). Theory choice and social choice: Kuhn versus Arrow. Mind, 120, 83–115.CrossRefGoogle Scholar
  18. Patty, J. W., & Penn, E. M. (2014). Social choice and legitimacy: The possibilities of impossibility. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  19. Regenwetter, M., Bernard Grofman, A. A. J., Marley, A. A. J., & Tsetlin, I. (2006). Behavioral social choice: Probabilistic models, statistical inference, and applications. Cambridge: Cambridge University Press.Google Scholar
  20. Riker, W. (1982). Liberalism against populism. New York, NY: Waveland Press.Google Scholar
  21. Saari, D. G. (2003). Capturing the ‘will of the people’. Ethics, 113(2), 333–349.CrossRefGoogle Scholar
  22. Schumpeter, J. (1942). Capitalism, socialism, and democracy. New York, NY: Harper & Brothers.Google Scholar
  23. Sen, A. (1973). On economic inequality. Oxford: Oxford University Press.CrossRefGoogle Scholar
  24. Sen, A. (1976). Poverty: An ordinal approach to measurement. Econometrica, 44(2), 219–231.CrossRefGoogle Scholar
  25. Sen, A. (1977). On weights and measures: Informational constraints in social welfare analysis. Econometrica, 45(7), 1539–1572.CrossRefGoogle Scholar
  26. Shepsle, K. A., & Weingast, B. R. (1981). Structure-induced equilibrium and legislative choice. Public Choice, 37(3), 503–519.CrossRefGoogle Scholar
  27. Waldron, J. (1999). Law and disagreement. Oxford: Oxford University Press.CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Political ScienceUniversity of CaliforniaSan DiegoUSA

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