| Affiliation: | (1) Ecole des Mines de Nantes, SUBATECH, La chanterie, 4 rue A Kastler, BP 20722, 44307 Nantes cedex 3, FRANCE;(2) GEMMA-UMR6154, Department of Economics, Université de Caen, Esplanade de la paix, 14032 Caen Cedex, FRANCE;(3) CNRS and GEMMA-UMR6154, MRSH bureau 230, Université de Caen, Esplanade de la Paix, 14032 Caen cedex, FRANCE;(4) Laboratoire de Mathématique, Applications et Physique Mathématique, UMR6628, Université d'Orléans, UFR des Sciences, 45067 Orléans Cedex 2, FRANCE |
| Abstract: | Summary. In a two candidate election, it might be that a candidate wins in a majority of districts while he gets less vote than his opponent in the whole country. In Social Choice Theory, this situation is known as the compound majority paradox, or the referendum paradox. Although occurrences of such paradoxical results have been observed worldwide in political elections (e.g. United States, United Kingdom, France), no study evaluates theoretically the likelihood of such situations. In this paper, we propose four probability models in order to tackle this issue, for the case where each district has the same population. For a divided electorate, our results prove that the likelihood of this paradox rapidly tends to 20% when the number of districts increases. This probability decreases with the number of states when a candidate receives significatively more vote than his opponent over the whole country.Received: 12 August 2002, Revised: 7 March 2003, JEL Classification Numbers: D71. Correspondence to: Vincent R. MerlinSpecial thanks are due to Franck Bisson, a Caen PhD student, who helped collect the data. The authors also gratefully acknowledge Ashley Piggins and an anonymous referee for their comments. |
