Fixed-budget and Multiple-issue Quadratic Voting

Abstract: Quadratic Voting (QV) is a social choice mechanism that addresses the "tyranny of the majority" of one-person-one-vote mechanisms. Agents express not only their preference ordering but also their preference intensity by purchasing $x$ votes at a cost of $x^2$. Although this pricing rule maximizes utilitarian social welfare and is robust against strategic manipulation, it has not yet found many real-life applications. One key reason is that the original QV mechanism does not limit voter budgets. Two variations have since been proposed: a (no-budget) multiple-issue generalization and a fixed-budget version that allocates a constant number of credits to agents for use in multiple binary elections. While some analysis has been undertaken with respect to the multiple-issue variation, the fixed-budget version has not yet been rigorously studied. In this work, we formally propose a novel fixed-budget multiple-issue QV mechanism. This integrates the advantages of both the aforementioned variations, laying the theoretical foundations for practical use cases of QV, such as multi-agent resource allocation. We analyse our fixed-budget multiple-issue QV by comparing it with traditional voting systems, exploring potential collusion strategies, and showing that checking whether strategy profiles form a Nash equilibrium is tractable.