Soc Choice Welf (2017) 49:315–327
The likelihood of a Condorcet winner in the logrolling
· Michel Le Breton
Received: 29 December 2016 / Accepted: 24 May 2017 / Published online: 1 June 2017
© Springer-Verlag Berlin Heidelberg 2017
Abstract The purpose of this note is to compute the probability of logrolling for
three different probabilistic cultures. The primary ﬁnding is that the restriction of
preferences to be in accord with the condition of separable preferences creates enough
additional structure among voters’ preference rankings to create an increase in the
likelihood that a Condorcet winner will exist with both IC and IAC-based scenarios.
However this increase is limited and the probabilities remain close to the conventional
probabilities of having a Condorcet winner when preferences are unrestricted.
Majority voting is one of the oldest pastimes of social choice theorists starting with
Condorcet (1785). It is well known that majority voting may lead to intransivities
We wish to thank the editor and the referees for their helpful comments. Some R programs have been
prepared and used to compute random approximations of the values of some of the probabilities
introduced in our paper. The codes of these programs are described in the working paper version of this
note available at https://www.tse-fr.eu/fr/research/publications/working-papers.
Michel Le Breton
University of Delaware, Newark, USA
Toulouse School of Economics and Institut Universitaire de France, Paris, France
CEMOI, Université de la Réunion, Saint-Denis, France