Abstract
According to the oft-repeated story, the theory of social choice was invented by the eighteenth century French mathematicians: Borda. Condorcet, and Laplace. After their contributions, the subject is said to have fallen into oblivion. The aim of this article is to challenge this narrative by reviewing a nineteenth century discussion on the merits of different voting rules. In that discussion the social choice results had a central role. The participants in the heated dispute were both professors at the University of Helsinki: Lorenz Lindelöf (1827–1908) was the Professor of Mathematics, a noted mathematician and statistician, while Johan Wilhelm Snellman (1806–1881) was the Professor of Philosophy and the unofficial intellectual leader of the Finnish national movement. Many of the arguments used by them also appear in modern treatments of social choice theory. Such basic anomalies of social choice as the Borda paradox, the Condorcet paradox, path-dependence, and strategic voting figured in the discussion.
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Notes
This was neither the first nor the last time that an academic nomination process stimulated the interest in the study of social choice. J. C. de Borda’s ground-breaking article ( 1995 [1770]) was intended to be a contribution to a discussion of the proper nomination method for the prestigious Institut de France, while Charles Dodgson’s writings on voting were inspired by the nomination processes of the Oxford colleges.
Similar “rules of three names” have been, and still are, quite common, especially in clerical contexts. On these rules and their strategic properties, see Barberà and Coelho (2010).
Circulaire till samtelige Collegier, Kongliga Brefet af den 6. Oktober 1746; my translation.
Lindlöf’s argument might be made more plausible by interpreting it in terms of a hypothetical contract. It may be argued that choosers who select a voting rule behind a veil of ignorance that excludes all information about preference intensities should rely on Laplace’s Principle and treat the distances between candidates as equal. That would justify the adoption of a Borda-like method. On contractarian arguments in voting theory, see e.g. Sugden (1981, pp. 132–145) or Riley (1990). Arguments for and against methods of the Borda type are discussed in detail in Lagerspetz (2016, pp. 95–113).
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Acknowledgments
The first versions of this text were presented in the seminar of the Public Choice Research Centre at the University of Turku (Finland), and in a seminar arranged by the Turku Club of Practical Philosophy. The author wants to thank all the participants, especially Hannu Nurmi, for their comments.
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Lagerspetz, E. Plurality, approval, or Borda? A nineteenth century dispute on voting rules. Public Choice 168, 265–277 (2016). https://doi.org/10.1007/s11127-016-0361-4
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DOI: https://doi.org/10.1007/s11127-016-0361-4