, Volume 3, Issue 1–2, pp 1–14 | Cite as

Deciding whether a law is constitutional, interpretable, or unconstitutional

  • Pablo Amorós
  • Ricardo Martínez
  • Bernardo Moreno
  • M. Socorro Puy
Open Access
Original Article


A high court has to decide whether a law is constitutional, unconstitutional or interpretable. The voting system is runoff. Runoff voting systems can be interpreted both, as social choice functions or as mechanisms. It is known that, for universal domains of preferences, runoff voting systems have several drawbacks as social choice functions. Although in our setting the preferences are restricted to be single-peaked over three alternatives, these problems persist. Runoff mechanisms are not well-behaved either: they do not implement any Condorcet consistent social choice function in undominated subgame perfect Nash equilibria. We show, however, that some Condorcet consistent social choice functions can be implemented in dominant strategies via other simple and natural mechanisms.


Runoff voting system Condorcet consistency Strategy-proofness Implementation theory 

JEL Classification

C72 D71 D78 



We thank Luis Corchón and two anonymous referees for their helpful comments. Financial assistance from Ministerio de Educación y Ciencia under project ECO2008-03674/ECON is gratefully acknowledged.


  1. Abreu D, Sen A (1990) Subgame perfect implementation: A necessary and sufficient condition. J Econ Theory 50: 285–299CrossRefGoogle Scholar
  2. Austen-Smith D, Banks JS (1996) Information aggregation, rationality and the Condorcet jury theorem. Amer Polit Sci Rev 90: 34–45CrossRefGoogle Scholar
  3. Barberà S (2010) Strategy-proof social choice, In: Arrow K, Suzumura K (eds) Handbook of social choice and welfare. vol 2. Kluwer Academic Publishers, Dordrecht (forthcoming)Google Scholar
  4. Bag PK, Sabourian H, Winter E (2009) Multi-stage voting, sequential elimination and Condorcet consistency. J Econ Theory 144: 1278–1299CrossRefGoogle Scholar
  5. Duggan J, Martinelli C (2001) A Bayesian model of voting in juries. Games Econ Behav 37: 259–294CrossRefGoogle Scholar
  6. Feddersen TJ, Pesendorfer W (1998) Convicting the innocent: The inferiority of unanimous jury verdict. Amer Polit Sci Rev 92: 23–35CrossRefGoogle Scholar
  7. Fishburn PC, Brams SJ (1981) Aproval voting, Condorcet’s principle, and runoff elections. Public Choice 36: 89–114CrossRefGoogle Scholar
  8. Gibbard A (1973) Manipulation of voting schemes: A general result. Econometrica 41: 587–601CrossRefGoogle Scholar
  9. Grofman B (2008) A taxonomy of runoff methods. Elect Stud 27: 395–399CrossRefGoogle Scholar
  10. Maskin E (1999) Nash equilibrium and welfare optimality. Rev Econ Stud 66: 23–38CrossRefGoogle Scholar
  11. Moore J, Repullo R (1988) Subgame perfect implementation. Econometrica 56: 1191–1220CrossRefGoogle Scholar
  12. Moulin H (1988) Axioms of cooperative decision making. Cambridge University Press, CambridgeCrossRefGoogle Scholar

Copyright information

© The Author(s) 2011

This article is published under license to BioMed Central Ltd. Open Acces This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Pablo Amorós
    • 1
  • Ricardo Martínez
    • 1
  • Bernardo Moreno
    • 1
  • M. Socorro Puy
    • 1
  1. 1.Departamento de Teoría e Historia EconómicaUniversidad de MálagaMálagaSpain

Personalised recommendations