Reflections on Two Old Condorcet Extensions
The distinction – in fact, rivalry – between two intuitive notions about what constitutes the winning candidates or policy alternatives has been present in the social choice literature from its Golden Age, i.e. in the late 18’th century . According to one of them, the winners can be distinguished by looking a the performance of candidates in one-on-one, that is, pairwise contests. According to the other, the winners are in general best situated in the evaluators’ rankings over all candidates. The best known class of rules among those conforming to the first intuitive notion are those that always elect the Condorcet winner whenever one exists. These rules are called Condorcet extensions for the obvious reason that they extend Condorcet’s well-known winner criterion beyond the domain where it can be directly applied. A candidate is a Condorcet winner whenever it defeats all other candidates in pairwise contests with a majority of votes. Condorcet extensions specify winners in all settings including those where a Condorcet winner is not to be found. Of course, in those settings where there is a Condorcet winner they all end up with electing it.
- 6.Felsenthal, D.S., Nurmi, H.: Monotonicity violations by Borda elimination and Nanson’s rules: a comparison Group Decis. Negot. 27, 637–664 (2018)Google Scholar
- 15.Nanson, E.J.: Methods of election. Trans. Proc. R. Soc. Vic., Art. XIX, 197–240 (1883)Google Scholar
- 18.Nurmi, H.: On Nanson’s method. In: Apunen, O., Borg, O., Hakovirta, H., Paastela, J. (eds.) Democracy in the Modern World. Essays for Tatu Vanhanen, Series A, vol. 260, pp. 199–210. Acta Universitatis Tamperensis, Tampere (1989)Google Scholar
- 23.Schwartz, T.: The Logic of Collective Choice. Columbia University Press, New York (1986)Google Scholar