Abstract
Condorcet was the first to show that it was possible for the results of voting to take some such form as a 1 beats a 2,a 2 beats a 3, a 3 beats a 1, and dealt extensively with these ‘contradictory cases’ as he called them. At a later date, Dodgson, working over the theory, also discovered this possibility and referred to the majorities in an instance like this as being ‘cyclical’, the motions ‘forming the cycle a 1 a 2 a 3 a 1’. Since no actual logical contradiction is involved, Condorcet’s term is unsatisfactory, while Dodgson’s aptly describes the facts, and we will retain it. Instances of such cycles have already been given.
This chapter is under considerable obligation to the Rev. C. L. Dodgson’s paper A Method of Taking Votes on More Than Two Issues (1876), which is reprinted at pp. 257–66.
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Notes
[In his revision copy DB gives two alternative proofs of this added proposition. We choose the simpler.]
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© 1998 Springer Science+Business Media New York
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McLean, I., McMillan, A., Monroe, B.L. (1998). Cyclical Majorities. In: McLean, I., McMillan, A., Monroe, B.L. (eds) The Theory of Committees and Elections by Duncan Black and Committee Decisions with Complementary Valuation by Duncan Black and R.A. Newing. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4860-3_7
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DOI: https://doi.org/10.1007/978-94-011-4860-3_7
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