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

Ernesto Savaglio () and Stefano Vannucci
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Ernesto Savaglio: University of Pescara
Stefano Vannucci: University of Siena

Social Choice and Welfare, 2019, vol. 52, issue 2, No 5, 295-327

Abstract: 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.

Date: 2019
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DOI: 10.1007/s00355-018-1148-y

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