In rank aggregation, the goal is to combine multiple input rankings into a single output ranking. In this paper, we analyze rank aggregation methods, so-called social welfare functions (SWFs), with respect to strategyproofness, which requires that no agent can misreport his ranking to obtain an output ranking that is closer to his true ranking in terms of the Kemeny distance. As our main result, we show that no anonymous SWF satisfies unanimity and strategyproofness when there are at least four alternatives. This result is proven by SAT solving, a computer-aided theorem proving technique, and verified by Isabelle, a highly trustworthy interactive proof assistant. Further, we prove by hand that strategyproofness is incompatible with majority consistency, a variant of Condorcet-consistency for SWFs. Lastly, we show that all SWFs in two natural classes have a large incentive ratio and are thus highly manipulable.
We propose a modal study of the notion of bisimulation. Our contribution is twofold. First, we extend the basic modal language with a new modality [b], whose intended meaning is universal quantification over all states that are bisimilar to the current one. We show that bisimulations are definable in this object language. Second, we provide a sound and complete axiomatisation of the class of all pairs of Kripke models linked by bisimulations.
