Stochastic Mechanisms for Truthfulness and Budget Balance in Computational Social Choice

In this thesis, we examine stochastic techniques for overcoming game theoretic and computational issues in the collective decision making process of self-interested individuals. In particular, we examine truthful, stochastic mechanisms, for settings with a strong budget balance constraint (i.e. there is no net flow of money into or away from the agents). Building on past results in AI and computational social choice, we characterise affinemaximising social choice functions that are implementable in truthful mechanisms for the setting of heterogeneous item allocation with unit demand agents. We further provide a characterisation of affine maximisers with the strong budget balance constraint. These mechanisms reveal impossibility results and poor worst-case performance that motivates us to examine stochastic solutions. To adequately compare stochastic mechanisms, we introduce and discuss measures that capture the behaviour of stochastic mechanisms, based on techniques used in stochastic algorithm design. When applied to deterministic mechanisms, these measures correspond directly to existing deterministic measures. While these approaches have more general applicability, in this work we assess mechanisms based on overall agent utility (efficiency and social surplus ratio) as well as fairness (envy and envy-freeness). We observe that mechanisms can (and typically must) achieve truthfulness and strong budget balance using one of two techniques: labelling a subset of agents as “auctioneers” who cannot affect the outcome, but collect any surplus; and partitioning agents into disjoint groups, such that each partition solves a subproblem of the overall decision making process. Worst-case analysis of random-auctioneer and random-partition stochastic mechanisms show large improvements over deterministic mechanisms for heterogeneous item allocation. In addition to this allocation problem, we apply our techniques to envy-freeness in the