Calculating the probability of the Condorcet Paradox using combinatorics tools

Speaker : Emma Caizergues
Date: 21/09/2022
Time: 3:00 pm - 4:00 pm
Location: Salle 4A120 - Palaiseau


The paradox of Condorcet (1785) is a phenomenon that occurs when people express their preferences amongst candidates. Calculating the limiting probability of the Condorcet paradox can be done by probabilistic methods. Krishnamoorthy and Raghavachari (2005) in particular, found results for the General Independent Culture. During this talk, I will first introduce some required knowledge in social choice theory and explain the problem. Then, I will focus on Krishnamoorthy and Raghavachari (2005) work to detail and clear up their results. Finally, I will present an analytic combinatorics method that permits to obtain the same kind of results. This will be the occasion to develop some classical technics of asymptotic analysis.


  • Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet. Essai sur
    l’application de l’analyse à la probabilité des décisions rendues à la pluralité
    des voix. Imprimerie royale, 1785.
  • Mukkai Krishnamoorthy and Madabhushi Raghavachari. Condorcet winner
    probabilities – A statistical perspective, 2005. URL