Plurality, approval, or Borda? A nineteenth century dispute on voting rules

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 Lindelof (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.