Viscous democracy is a generalization of liquid democracy, a social choice framework in which voters may transitively delegate their votes. In viscous democracy, a "viscosity" factor decreases the weight of a delegation the further it travels, reducing the chance of excessive weight flowing between ideologically misaligned voters. We demonstrate that viscous democracy often significantly improves the quality of group decision-making over liquid democracy. We first show that finding optimal delegations within a viscous setting is NP-hard. However, simulations allow us to explore the practical effects of viscosity. Across social network structures, competence distributions, and delegation mechanisms we find high viscosity reduces the chance of “super-voters” attaining large amounts of weight and increases the number of voters that are able to affect the outcome of elections. This, in turn, improves group accuracy as a whole. As a result, we argue that viscosity should be considered a core component of liquid democracy.

Given a set of items and a set of evaluators who all individually rank them, how do we aggregate these evaluations into a single societal ranking? Work in social choice and statistics has produced many aggregation methods for this problem, each with its desirable properties, but also with its limitations. Further, existing impossibility results rule out designing a single method that achieves every property of interest. Faced with this trade-off between incompatible desiderata, how do we decide which aggregation rule to use, i.e., what is a good rule picking rule? In this paper, we formally address this question by introducing a novel framework for rule picking rules (RPRs). We then design a data-driven RPR that identifies the best aggregation method for each specific setting, without assuming any generative model. The principle behind our RPR is to pick the rule which maximizes the consistency of the output ranking if the data collection process were repeated. We introduce several consistency-related axioms for RPRs and show that our method satisfies them, including those failed by a wide class of natural RPRs. While we prove that the algorithmic problem of maximizing consistency is computationally hard, we provide a sampling-based implementation of our RPR that is efficient in practice. We run this implementation on known statistical models and find that, when possible, our method selects the maximum likelihood estimator of the data. Finally, we show that our RPR can be used in many real-world settings to gain insights about how the rule currently being used can be modified or replaced to substantially improve the consistency of the process. Taken together, our work bridges an important gap between the axiomatic and statistical approaches to rank aggregation, laying a robust theoretical and computational foundation for principled rule picking.

Committee-selection problems arise in many contexts and applications, and there has been increasing interest within the social choice research community on identifying which properties are satisfied by different multi-winner voting rules. In this work, we propose a data-driven framework to evaluate how frequently voting rules violate axioms across diverse preference distributions in practice, shifting away from the binary perspective of axiom satisfaction given by worst-case analysis. Using this framework, we analyze the relationship between multi-winner voting rules and their axiomatic performance under several preference distributions. We then show that neural networks, acting as voting rules, can outperform traditional rules in minimizing axiom violations. Our results suggest that data-driven approaches to social choice can inform the design of new voting systems and support the continuation of data-driven research in social choice.

Recently, social choice theory has been found broadly useful for AI alignment and evaluation, often based on the axiomatic properties for combining preferences provided by social choice functions. However, for many sets of axioms, functions which never violate the axioms are known to not exist, e.g., Arrow’s Impossibility Theorem. Recent work on learning novel rules to minimize axiom violations shows the effectiveness of machine learning but explores a limited class of axioms. In this work we show the effectiveness of standard social choice data structures as features for learning existing voting rules, resulting in networks that have better accuracy than past approaches while using an order of magnitude fewer parameters. Subsequently, we develop a process for adding axiomatic properties to existing voting rules. By building novel axiomatic loss functions we are able to use transfer learning to fine-tune existing voting rules in a way that quantitatively preserves their original behaviour while also exhibiting strong adherence to previously absent axiomatic properties, resulting in novel voting rules that are closer to the impossibility frontier than those in the machine learning or theoretical literature.