Liquid Democracy with Ranked Delegations

Abstract

Liquid democracy is a novel paradigm for collective decision-making that gives agents the choice between casting a direct vote or delegating their vote to another agent. We consider a generalization of the standard liquid democracy setting by allowing agents to specify multiple potential delegates, together with a preference ranking among them. This generalization increases the number of possible delegation paths and enables higher participation rates because fewer votes are lost due to delegation cycles or abstaining agents. In order to implement this generalization of liquid democracy, we need to find a principled way of choosing between multiple delegation paths. In this paper, we provide a thorough axiomatic analysis of the space of delegation rules, i.e., functions assigning a feasible delegation path to each delegating agent. In particular, we prove axiomatic characterizations as well as an impossibility result for delegation rules. We also analyze requirements on delegation rules that have been suggested by practitioners, and introduce novel rules with attractive properties. By performing an extensive experimental analysis on synthetic as well as real-world data, we compare delegation rules with respect to several quantitative criteria relating to the chosen paths and the resulting distribution of voting power. Our experiments reveal that delegation rules can be aligned on a spectrum reflecting an inherent trade-off between competing objectives.

Unravelling Expressive Delegations: Complexity and Normative Analysis

“…They study the properties of breadth-first search and depth-first search in this context. Their model inspired a number of recent papers (Colley, Grandi, and Novaro 2022;Brill et al 2022;Kavitha et al 2020;Utke and Schmidt-Kraepelin 2023); in particular, the work of Colley et al extends the model of Kotsialou and Riley (2020) to more expressive ballots and is the direct predecessor of our work. Brill et al (2022) define the concept of delegation graphs, for which unravelling procedures are called delegation rules.…”

“…Their model inspired a number of recent papers (Colley, Grandi, and Novaro 2022;Brill et al 2022;Kavitha et al 2020;Utke and Schmidt-Kraepelin 2023); in particular, the work of Colley et al extends the model of Kotsialou and Riley (2020) to more expressive ballots and is the direct predecessor of our work. Brill et al (2022) define the concept of delegation graphs, for which unravelling procedures are called delegation rules. They study two important subclasses: sequence rules and confluent rules; the latter corresponding to selecting an arborescence of the graph.…”

“…This approach has the attractive feature of explainability: The collection of positions c = (c a ) a∈N forms a certificate, which can be reported together with the electoral outcome as an explanation for it. Unravelling procedures that work in this fashion are called confluent (Brill et al 2022). They provide a high degree of accountability, as each agent can see whether their direct vote τ a was used, or which other agent their vote was delegated to.…”

Incentivizing free riders improves collective intelligence in social dilemmas

“…Understanding how incentives may affect collective intelligence is particularly important for testing new voting systems, such as liquid democracy ( 40 ). Campbell et al ( 13 ) show that collective intelligence decreases with liquid democracy because people tend to delegate too much, reducing the effective sample size for crowd wisdom.…”

A Voting Power Measure for Liquid Democracy with Multiple Delegation

“…In this model, agents provide a ranking over multiple delegations, and this information is used as a backup to solve possible delegation cycles. With a similar approach, we can mention [9,10], where the delegation of power to multiple agents is studied through a ranking of preferences. Finally, we mention [16], where a technique based on fluid dynamics is proposed in order to choose a delegation graph based on the preferences of the agents.…”