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Social Choice and Welfare

, Volume 52, Issue 2, pp 295–327 | Cite as

Strategy-proof aggregation rules and single peakedness in bounded distributive lattices

  • Ernesto SavaglioEmail author
  • Stefano Vannucci
Original Paper
  • 74 Downloads

Abstract

It is shown that, under a very comprehensive notion of single peakedness, an aggregation rule on a bounded distributive lattice is strategy-proof on any rich domain of single peaked total preorders if and only if it admits one of three distinct and mutually equivalent representations by lattice-polynomials, namely whenever it can be represented as a generalized weak consensus rule, a generalized weak sponsorship rule , or an iterated medianrule. The equivalence of individual and coalitional strategy-proofness that is known to hold for single peaked domains in bounded linearly ordered sets and in finite trees typically fails in such an extended setting. A related impossibility result concerning non-trivial anonymous and coalitionally strategy-proof aggregation rules is also obtained.

Notes

Acknowledgements

Thanks are due to an Associate Editor and two Anonymous reviewers for their most helpful and constructive criticisms and comments. The usual disclaimer applies.

Supplementary material

355_2018_1148_MOESM1_ESM.pdf (326 kb)
Supplementary material 1 (pdf 326 KB)

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.DECUniversity of PescaraPescaraItaly
  2. 2.DEPSUniversity of SienaSienaItaly

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