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A counterexample to Dhillon (1998)

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Abstract

We provide a counterexample to Theorem 1 (A) in Dhillon (Soc Choice Welf 15:521–542, 1998).

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Notes

  1. We assume that the reader is familiar with the definitions and notation in Dhillon (1998).

  2. The omitted condition is that the domain of the SWF needs to be restricted to preference profiles that can be represented by profiles of utility functions satisfying the condition \(d(\mathbf {u})>2\). We are grateful to Amrita Dhillon for confirming that this is the correct interpretation of her Theorem 1(A), and that also our re-formulation of the Extended Pareto Axiom above reflects her intentions.

  3. Here and in the following we identify utility functions \(u:A\rightarrow \mathbb {R}\) with the real vector \((u(a))_{a\in A}\).

  4. Detailed derivations of Eqs. (4), (10), (7), (13), and (14) are available online.

  5. We abuse the symbol \(\lambda _i\) to denote not only the function \(\lambda _i: {\mathscr {L}}\rightarrow \mathbb {R}_{++}\) but also numbers \(\lambda _i>0\).

References

  • Arrow KJ (1951) Social choice and individual values. Wiley, New York

    Google Scholar 

  • Börgers T, Choo Y-M (2015) Revealed relative utilitarianism. University of Michigan, Ann Arbor

    Google Scholar 

  • Dhillon A (1998) Extended Pareto rules and relative utilitarianism. Soc Choice Welf 15:521–542

    Article  Google Scholar 

  • Dhillon A, Mertens J-F (1999) Relative utilitarianism. Econometrica 67:471–498

    Article  Google Scholar 

  • Harsanyi J (1955) Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. J Political Econ 63:309–321

  • Hylland A (1980) Aggregation procedure for cardinal preferences: a comment. Econometrica 48:539–542

    Article  Google Scholar 

  • Kalai E, Schmeidler D (1977) Aggregation procedure for cardinal preferences: a formulation and proof of Samuelson’s impossibility conjecture. Econometrica 45:1431–1438

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Economics, University of Michigan, Ann Arbor, USA

    Tilman Börgers

  2. Singapore, Singapore

    Yan-Min Choo

Authors
  1. Tilman Börgers
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  2. Yan-Min Choo
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Corresponding author

Correspondence to Tilman Börgers.

Additional information

We are grateful to Amrita Dhillon for conversations about this note.

Electronic supplementary material

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Supplementary material 1 (pdf 110 KB)

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Börgers, T., Choo, YM. A counterexample to Dhillon (1998). Soc Choice Welf 48, 837–843 (2017). https://doi.org/10.1007/s00355-017-1037-9

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  • DOI: https://doi.org/10.1007/s00355-017-1037-9

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