The (In)Vulnerability of 20 Voting Procedures to the Inconsistency Paradox (aka Reinforcement Paradox) in a Restricted Domain

  • Dan S. Felsenthal
  • Hannu NurmiEmail author
Part of the SpringerBriefs in Economics book series (BRIEFSECONOMICS)


This chapter focuses on the possibility that some well-known voting procedures are vulnerable to the Inconsistency paradox even in preference profiles that are characterized by a restricted domain where a Condorcet winner exists and is elected in each disjoint subset of voters but not in their union. Our focus is on 15 voting procedures known to be vulnerable to the Inconsistency paradox in unrestricted domains. These procedures include 10 Condorcet-consistent and 5 Condorcet-non-consistent rules. The former are, however, only briefly touched upon because their invulnerability to the Inconsistency paradox in the restricted domain is obvious.


Voting paradoxes Inconsistency voting paradox Restricted domains Condorcet-consistent procedures Condorcet non-consistent procedures Variable electorates 


  1. Felsenthal, D. S., & Nurmi, H. (2018). Voting procedures for electing a single candidate: Proving their (in)vulnerability to various voting paradoxes. Cham, Switzerland: Springer.CrossRefGoogle Scholar
  2. Young, H. P. (1974). An axiomatization of Borda’s rule. Journal of Economic Theory, 9, 43–52.CrossRefGoogle Scholar

Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Philosophy, Contemporary History and Political ScienceUniversity of TurkuTurkuFinland

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