Top-Pair and Top-Triple Monotonicity (original) (raw)

Abstract

We say that a social choice function (SCF) satisfies Top-k Monotonicity if the following holds. Suppose the outcome of the SCF at a preference profile is one of the top _k_-ranked alternatives for voter i. Let the set of these k alternatives be denoted by B. Suppose that _i_’s preference ordering changes in such a way that the set of first _k_-ranked alternatives remains the set B. Then the outcome at the new profile must belong to B. This definition of monotonicity arises naturally from considerations of set “improvements” and is weaker than the axioms of strong positive association and Maskin Monotonicity. Our main results are that if there are two voters then a SCF satisfies unanimity and Top-2 or Top-pair Monotonicity if and only if it is dictatorial. If there are more than two voters, then Top-pair Monotonicity must be replaced by Top-3 Monotonicity (or Top-triple Monotonicity) for the analogous result. Our results demonstrate that connection between dictatorship and “improvement” axioms is stronger than that suggested by the Muller–Satterthwaite result (Muller and Satterthwaite in J Econ Theory 14:412–418, 1977) and the Gibbard–Sattherthwaite theorem.

Access this article

Log in via an institution

Subscribe and save

• Starting from 10 chapters or articles per month
• Access and download chapters and articles from more than 300k books and 2,500 journals
• Cancel anytime View plans

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

• Aswal N, Chatterjee S, Sen A (2003) Dictatorial domains. Econ Theory 22:45–62
  Article Google Scholar
• Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41:587–601
  Article Google Scholar
• Maskin E (1999) Nash equilibrium and welfare optimality. Rev Econ Stud 66:23–38
  Article Google Scholar
• Moulin H (1983) The strategy of social choice. North-Holland
• Muller E, Satterthwaite M (1977) The equivalence of strong positive association and strategy proofness. J Econ Theory 14:412–418
  Article Google Scholar
• Nehring K (2000) Monotonicity implies generalized strategy-proofness for correspondences. Soc Choice Welfare 17:367–375
  Article Google Scholar
• Satterthwaite M (1975) Strategy-proofness and arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10:187–217
  Article Google Scholar
• Reny P (2001) Arrow’s theorem and Gibbard–Satterthwaite theorem: a unified approach. Econ Lett 70:99–105
  Article Google Scholar

Download references

Author information

Authors and Affiliations

1. Concordia University, Montreal, Canada
   Dipjyoti Majumdar
2. Indian Statistical Institute, New Delhi, India
   Arunava Sen

Authors

1. Dipjyoti Majumdar
2. Arunava Sen

Corresponding author

Correspondence toArunava Sen.

Rights and permissions

About this article

Cite this article

Majumdar, D., Sen, A. Top-Pair and Top-Triple Monotonicity.Soc Choice Welfare 27, 175–187 (2006). https://doi.org/10.1007/s00355-006-0119-x

Download citation

• Received: 10 July 2003
• Accepted: 07 February 2005
• Published: 12 April 2006
• Issue date: August 2006
• DOI: https://doi.org/10.1007/s00355-006-0119-x

Keywords