The Geometry of Decision-Making in DAOs: An Information-Theoretic Mapping of Consensus and Disagreement in Decentralized Token Voting

Abstract

Decentralized Autonomous Organizations (DAOs) are digital communities that make collective decisions by voting on blockchain communication-systems, amongst other coordination media. "Token voting" is intended to, on the one hand, efficiently synthesize individuals' limited information toward collective intelligence, on the other, it is presented as an inclusive approach to the governance of organizations-allowing any member with tokens to voice their opinions. In this latter sense, DAO decision-making is described as 'decentralized governance,' a misnomer, as most DAOs exhibit extreme centralization in token allocation. Yet, this paper finds value in DAO's collective decision-making intentions: the core blockchain infrastructure, when paired with a DAO's collective voting, produces an immutable, peerproduced ledger of group decision-making. Much empirical and theoretical attention has focused on consensus, understood as the majority-supported outcome of a vote. This paper argues that such a focus is incomplete. Consensus is often treated as a signal of a collective's certainty in a chosen outcome, yet this certainty depends on the structure of the decision space. The same majority share can imply different levels of certainty depending on the number of available options and how support is distributed across non-winning alternatives. As such, collective decisions cannot be evaluated by majority size alone, but must be understood relative to how a community allocates support across the full set of choices. To this end, this paper proposes the Rényi family of entropy-based measures, along with several derived metrics, as tools to map the topology of consensus and disagreement. It applies these metrics to voting data from 277 DAOs to signal (1) whether dissenting opinions converge into coordinated blocks of collective opposition or disperse pluralistically across the decision space, and (2) the effective number of choices and relative weight of substantively engaged alternatives within the choice set. The former heuristic qualifies the type of disagreement to ask "did disagreement converge into viable minority alternatives?" The latter heuristic quantifies the number of options that were seriously considered, and to what degree?" Altogether, this paper contributes a formal information-theoretic framework for representing the topology of collective decision-making through the distribution of support across all alternatives. It provides heuristics that treat a community's decision-making quality as a design question and enables majority outcomes to be interpreted relative to how support is distributed across the full set of choices, rather than in isolation.