The borda and condorcet principles: Three medieval applications

We report three medieval works, hitherto unknown to social choice, which discuss procedures for elections when there are more than two candidates. Two of the three propose Borda methods and the third a Condorcet method of successive pairwise comparison. All three discuss problems of manipulation. One of them displays a matrix for pairwise comparisons; this is a work written in 1299, nearly 600 years before the matrix notation was believed to have been invented by C. L. Dodgson. We conclude with a review of the theory of voting in medieval Europe.We acknowledge with gratitude the support of the Leverhulme Trust for IMcL's work on the history of social choice; William Riker for an initial lead on Nicolas Cusanus; Alexander Murray for translating Cusanus and reviewing IMcL's translation of Lull's Latin text; and Robert Pring-Mill for reviewing JL's translation of Lull's Catalan text.