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Intensity Comparisons, the Borda Rule and Democratic Theory

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Abstract

The standard democratic methods are unable to take the intensities of preferences into account. This is seen as a problem both in the theory of social choice and in the philosophy of democracy. The Borda count is sometimes defended as a rule which is able to take intensity differences into account. Here, it is argued that some defences of the Borda rule are based on the view that the basic task of voting rules is to aggregate information. In voting, however, there are two aspects which are not equally relevant other contexts: the requirements of democracy, and the interaction between the aggregation method and the input of aggregation. Voting should be conceptualized as an exercise of power. Arguments for Borda may be convincing in some contexts, but not necessarily in voting contexts.

An earlier version of this chapter was published in Essays in Honor of Hannu Nurmi (Homo Oeconomicus 28:49–70), 2011.

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Notes

  1. 1.

    This text is a slightly revised version of a chapter (with the same title) published in Homo Oeconomicus 28 (2011), pp. 49–70. I am grateful to the two anonymous referees of the journal for their valuable criticism, and to Hannu Nurmi and Manfred J. Holler for useful comments.

  2. 2.

    The discussion on the fundamental values of democracy has to be saved to another occasion. There is a vast amount of literature on the subject; for an interested reader, I may recommend the books of Christiano (1996) and Saward (1998) as good starting points. (As the reader may guess, the position taken in those works is quite close to my own.)

  3. 3.

    The Borda rule was already described by the great philosopher and theologician Nicolaus Cusanus in his Concordantia catholica (1433/1995) where it was recommended as the best method to choose the Emperor. According to Antony Black (1994, p. 39), the Council of Basle (1431–49), in which Cusanus was a member, actually used a Borda-like rule. In Belgium, a Borda-like preferential rule was used in clerical elections from the sixteenth to the eighteenth century, although the weights were not same as in Borda: one first-preference vote was worth of two second-preference votes or three third-preference votes (Moulin 1958, p. 547). The interpretation of the electoral results caused some disagreements. Pope Gregory XV (pope 1621–1623) decided that when “the number of votes” and “the number of voters” pointed in different directions, the latter was decisive (ibid., p. 517). This is the first recorded conflict between these two criteria of preference-aggregation.

  4. 4.

    In an early paper (Lagerspetz 1988) I argued that the main methodological difference between the natural and the social sciences is related to this possibility.

  5. 5.

    Fishkin’s “deliberative poll” (Fiskin 1991) operates with a randomly selected demos. However, although he recommends its use as an aid in democratic decision-making, he does not propose that it should replace general elections.

  6. 6.

    Fishkin (1991, p. 83) quotes a study on opinion measurements: “Most respondents feel obliged to have an opinion, in effect, to help the interviewer out. (…) In effect, opinions are invented on the spot”.

  7. 7.

    This counterargument was made by Manfred J. Holler.

Literature

  • Baharad., E., & Nitzan, S. (2005). Approval voting reconsidered. Economic Theory, 26, 619–628.

    Google Scholar 

  • Black, A. (1994). Diplomacy, doctrine and the disintegration. In J. Helmrath & H. Müller (Eds.), Studien zum 15. Jahrhundert: Festschrift für Erich Meuthen. München: R. Oldenbourg.

    Google Scholar 

  • Brennan, G., & Lomasky, L. (1993). Democracy and decision. The pure theory of electoral preference. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Buchanan, J. M., & Tullock, G. (1962). The Calculus of Consent. Ann Arbor: University of Michigan Press.

    Google Scholar 

  • Budge, I. (1996). The new challenge of direct democracy. Cambridge: Polity Press.

    Google Scholar 

  • Budge, I. (2000). Deliberative democracy versus direct democracy—plus political parties! In M. Saward (Ed.), Democratic innovation deliberation, representation and association. London: Routledge.

    Google Scholar 

  • Christiano, T. (1996). The rule by the many. Boulder: Westwiew Press.

    Google Scholar 

  • Cox, G. (1997). Making votes count: Strategic coordination in the world’s electoral systems. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Dabagh, T. S. (1934). The vote-and-a-half system of majority choice by plurality rule. The American Political Science Review, 28, 93–101.

    Article  Google Scholar 

  • Dahl, R. A. (1956). A preface to democratic theory. Chicago: University of Chicago Press.

    Google Scholar 

  • Doron, G. (1979). Is the hare voting scheme representative ? The Journal of Politics, 41, 918–922.

    Article  Google Scholar 

  • Dummett, M. (1984). Voting procedures. Oxford: Oxford University Press.

    Google Scholar 

  • Dummett, M. (1997). The principles of electoral reform. Oxford: Oxford University Press.

    Google Scholar 

  • Feldman, A. M. (1980). Welfare economics and social choice. Boston: Martinus Nijhoff.

    Book  Google Scholar 

  • Fishkin, J. S. (1991). Democracy and deliberation. New directions for democratic reform. New Haven: Yale University Press.

    Google Scholar 

  • Härd, S. (1999). Den godtyckliga demokratin: En studie av olika metoder att tilgodse kravet om proportionalitet. Uppsala: Uppsala University Library.

    Google Scholar 

  • Härd, S. (2000). Arbitrary democracy. In N. Berggren, N. Karlson, & J. Nergelius (Eds.), Why constitutions matter. Stockholm: City University Press.

    Google Scholar 

  • Harsanyi, J. (1979). Bayesian decision theory, rule utilitarianism and Arrow’s impossibility theorem. Theory and Decision, 11, 280–317.

    Article  Google Scholar 

  • Hillinger, C. (2004). On the possibility of democracy and rational collective choice, http://epub.ub.uni-muenchen.de/429/1/DEMOCRACY.pdf.

  • Hillinger, C. (2005). The case for utilitarian voting. Homo Oeconomicus, 22, 295–321.

    Google Scholar 

  • Jones, P. (1988). Intense preferences, strong beliefs and democratic decision-making. Political Studies, 36, 7–29.

    Article  Google Scholar 

  • Karvonen, L. (2004). The Achilles’ heel of democracy? on majority and intensity. In M. Wiberg (Ed.), Reasoned choices (pp. 242–263). Turku: The Finnish Political Science Association.

    Google Scholar 

  • Kendall, W., & Carey, G. W. (1968). The intensity problem and democratic theory. The American Political Science Review, 62, 5–24.

    Article  Google Scholar 

  • Lagerspetz, E. (1988). Reflexive predictions and strategic actions. Social Science Information, 27, 307–320.

    Article  Google Scholar 

  • Lagerspetz, E. (2004). Evaluating voting systems. In M. Wiberg (Ed.), Reasoned choices (pp. 201–222). Turku: The Finnish Political Science Association.

    Google Scholar 

  • Lehtinen, A. (2007). A farewell to Arrow’s theorem. http://philsci-archive.pitt.edu/archive/00003429/01/fiia.pdf.

  • Mackie, G. (2003). Democracy defended. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • MacKay, A. (1980). Arrow’s theorem. The paradox of social choice, a case study in the philosophy of economics, London: Yale University Press.

    Google Scholar 

  • McLean, I. (1991). Forms of representation and systems of voting. In D. Held (Ed.), Political theory today (pp. 172–196). Cambridge: Polity Press.

    Google Scholar 

  • Moulin, L. (1958), “Sanior et maior pars. Note sur l’evolution des techniques électorales dans les ordres religieux du VIe au XIIIe siècle,” Revue historique de droit Français et étranger 35:368–397, 491–529.

    Google Scholar 

  • Nicholaus of Cusa [Nicolaus Cusanus] (1434/1995), The Catholic concordance, ed. P. E. Sigmund, Cambridge: Cambridge University Press.

    Google Scholar 

  • Ng, Y.-K. (1979). Welfare economics. Introduction and development of basic concepts. London: Macmillan.

    Google Scholar 

  • Nurmi, H. (2007). Assessing Borda’s rule and its modifications. In P. Emerson (Ed.), Designing an all-inclusive democracy. Consensual voting procedures for use in parliaments, councils and committees (pp. 109–119). Berlin: Springer.

    Chapter  Google Scholar 

  • Rawls, J. (1971). A theory of justice. Oxford: Oxford University Press.

    Google Scholar 

  • Reilly, B. (2002). Social choice in the south seas: Electoral innovation and the Borda count in the Pacific Island Countries. International Political Science Review, 23, 355–372.

    Article  Google Scholar 

  • Riley, J. (1988). Liberal Utilitarianism. Social choice and J.S. Mill’s philosophy, Cambridge: Cambridge University Press.

    Google Scholar 

  • Riley, J. (1990). Utilitarian ethics and democratic government. Ethics, 100, 335–348.

    Article  Google Scholar 

  • Riker, W. H., & Ordeshook, P. C. (1973). An introduction to positive political theory. Englewood Cliffs: Prentice Hall.

    Google Scholar 

  • Saari, D. G. (1995). Inner consistency or not inner consistency: A reformulation is the answer. In W. A. Barnett, H. Moulin, M. Salles, & N. Schofield (Eds.), Social choice, welfare and ethics (pp. 187–212). Cambridge: Cambridge University Press.

    Google Scholar 

  • Saari, D. G. (2001). Decisions and elections. Explaining the unexpected. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Sager, T. (2002). Democratic planning and social choice dilemmas. Prelude to institutional planning theory. Aldershot: Ashgate.

    Google Scholar 

  • Sartori, G. (1987). The theory of democracy revisited. Part One: The contemporary debate. New Jersey: Chatham House Publishers.

    Google Scholar 

  • Saward, M. (1998). The terms of democracy. Cambridge: Polity Press.

    Google Scholar 

  • Schwartz, T. (1986). The logic of collective choice. New York: Columbia University Press.

    Google Scholar 

  • Scott, M. J. and Zivikovic, I (2003). “On Rank Reversals in the Borda Count,” Proceedings of DETC 2003, Chicago: The 2003 ASME Design Engineering Technical Conferences. http://design.me.uic.edu/mjscott/papers/dtm48674.pdf.

  • Sen, A. K. (1982). Interpersonal Comparisons of Welfare. In A. K. Sen (ed.), Choice, Welfare and Measurement, Oxford: Blackwell, 264–281.

    Google Scholar 

  • Serais, J. (2008). Cloning manipulation of the Borda rule. http://www.hss.caltech.edu/Events/SCW/papers/seraj.pdf.

  • Sugden, R. (1981). The political economy of public choice: An introduction to welfare economics. Oxford: Martin Robertson.

    Google Scholar 

  • Tännsjö, T. (1992). Populist democracy: A defence. London: Routledge.

    Google Scholar 

  • Van det Hout, E., de Swart, H., & ter Veer, A. (2006). Characteristic properties of list proportional representation systems. Social Choice and Welfare, 27, 459–475.

    Article  Google Scholar 

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Lagerspetz, E. (2013). Intensity Comparisons, the Borda Rule and Democratic Theory. In: Holler, M., Nurmi, H. (eds) Power, Voting, and Voting Power: 30 Years After. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35929-3_6

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