Designing Strategyproof Election Systems with Score Voting (2210.02496v1)

Abstract: We focus on the strategyproofness of voting systems where voters must choose a number of options among several possibilities. These systems include those that are used for Participatory Budgeting, where we organize an election to determine the allocation of a community's budget (city, region, etc.) dedicated to the financing of projects. We present a model for studying voting mechanisms and the Constrained Change Property (CCP), which will be used to design voting mechanisms that are always strategyproof. We also define a new notion of social choice function and use it to design a new class of utilitarian voting mechanisms that we call score voting. We prove that the mechanisms designed with core voting with a neutral score function are equivalent to knapsack voting on the same instance and that any score voting designed with a total score function is strategyproof if and only if its score function satisfies CCP. These results are combined to devise an algorithm that can find the closest total score function that makes any given score voting to be strategyproof.