Non-manipulability in Set-valued and Probabilistic Social Choice Theory

A fundamental requirement in social choice theory is non-manipulability, i.e., voters should not be able to benefit by voting dishonestly. Unfortunately, a seminal result by Gibbard [12] and Satterthwaite [15] states that only extremely unattractive voting rules can be strategyproof if it is required to choose a single winner deterministically. Two common approaches for circumventing this impossibility are to allow for sets of winners and to allow for randomization. It is for both approaches possible to define various strategyproofness notions based on different assumptions on how voters compare sets of alternatives or lotteries on alternatives, and consequently, both positive and negative results can be obtained. The goal of this PhD project is to analyze for both models the boundary between possibility and impossibility results for various strategyproofness notions.