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

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