Token-based Voting Systems

Abstract

Token-based voting systems are increasingly adopted in digital governance contexts such as decentralized autonomous organizations and participatory budgeting, yet their standard aggregation rules often lead to undesirable outcomes, including oligarchic dominance or voter apathy. This paper introduces a general mathematical framework for token-based voting that interpolates between one-person-one-vote and one-token-onevote paradigms through the notion of radical voting functions. These functions map voting tokens to actual votes via concave transformations that preserve incentives for participation while compressing excessive voting power. We formalize consensus as an aggregation of transformed votes and study its structural properties using tools from convex analysis and majorization theory. We show that radical voting functions reward broad and evenly distributed support and penalize highly concentrated voting patterns, thereby favoring pluralistic outcomes over individualistic ones. Quadratic voting emerges as a special case within this framework, characterized by linear marginal voting costs. The analysis is extended to account for voter heterogeneity by incorporating similarity measures into the consensus function, linking voting outcomes to diversity among participants. Overall, the framework provides a principled foundation for designing voting mechanisms that balance merit, inclusiveness, and resistance to capture in token-based governance systems.