Liquid Democracy: An Algorithmic Perspective

Kahng, Anson; Mackenzie, Simon; Procaccia, Ariel D.

doi:10.1609/aaai.v32i1.11468

Cited by 37 publications

(24 citation statements)

References 11 publications

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“…They find that adding a cost polynomial in the number of representatives and a benefit of choosing the correct outcome polynomial in the number of voters decreases the optimal congress size to O(log n). Finally, this work supports, to some extent, propositions to constitute assemblies of citizens under fluid democracy (Miller 1969;Blum and Zuber 2016;Green-Armytage 2015;Christoff and Grossi 2017;Kahng, Mackenzie, and Procaccia 2021;Gölz et al 2018;Halpern et al 2021) that would vote on behalf of the entire population. Indeed, fluid democracy could yield very large citizen assemblies deemed desirable by our findings.…”

Section: Discussionsupporting

confidence: 77%

How Many Representatives Do We Need? The Optimal Size of a Congress Voting on Binary Issues

Revel

Lin

Halpern

2022

AAAI

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Aggregating opinions of a collection of agents is a question of interest to a broad array of researchers, ranging from ensemble-learning theorists to political scientists designing democratic institutions. This work investigates the optimal number of agents needed to decide on a binary issue under majority rule. We take an epistemic view where the issue at hand has a ground truth ``correct'' outcome and each one of n voters votes correctly with a fixed probability, known as their competence level or competence. These competencies come from a fixed distribution D. Observing the competencies, we must choose a specific group that will represent the population. Finally, voters sample a decision (either correct or not), and the group is correct as long as more than half the chosen representatives voted correctly. Assuming that we can identify the best experts, i.e., those with the highest competence, to form an epistemic congress we find that the optimal congress size should be linear in the population size. This result is striking because it holds even when allowing the top representatives to become arbitrarily accurate, choosing the correct outcome with probabilities approaching 1. We then analyze real-world data, observing that the actual sizes of representative bodies are much smaller than the optimal ones our theoretical results suggest. We conclude by examining under what conditions congresses of sub-optimal sizes would still outperform direct democracy, in which all voters vote. We find that a small congress would beat direct democracy if the rate at which the societal bias towards the ground truth decreases with the population size fast enough, and we quantify the speed needed for constant and polynomial congress sizes.

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Section: Discussionsupporting

confidence: 77%

How Many Representatives Do We Need? The Optimal Size of a Congress Voting on Binary Issues

Revel

Lin

Halpern

2022

AAAI

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“…Their objective is to assign delegations in such a way as to minimize the maximal voting weight of agents. Kahng, Mackenzie, and Procaccia (2021) consider an epistemic setting in which each agent has a competence level (i.e., probability of making the "correct" voting decision) and an approved subset of other agents. They are interested in (possibly randomized) delegation mechanisms that increase the likelihood of a correct decision compared to direct voting.…”

Section: Related Workmentioning

confidence: 99%

Liquid Democracy with Ranked Delegations

Brill

Delemazure

George

et al. 2022

AAAI

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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.

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“…Several works have argued that these super-voters are or could be detrimental. Within the theoretical model of voter competence in Kahng et al [19], super-voters can make liquid democracy less likely than direct democracy to choose the correct outcome in the worst-case due to a wisdom of the crowd effect. On the practical side, Kling et al [20] observed that the presence of super-voters may have discouraged other voters from participating, but ultimately concluded that, "While we find that the theoretical and potential power of super-voters is indeed high, we also observe that they stabilise the voting system and prevent stagnation while they use their power wisely.…”

Section: 24mentioning

confidence: 99%

“…Originally championed by Charles Dodgson (AKA Lewis Carroll) in 1884 [8,25], liquid democracy is an old idea that has attracted renewed interest from both computer science [4,5,7,14,19,21,26] and political philosophy [3] perspectives. The basic concept is simple: it is a voting system in which each agent can choose to either vote directly or delegate their vote(s) to another agent.…”

Section: Introductionmentioning

confidence: 99%

“…As liquid democracy has become a topic of serious study in the computer science and artificial intelligence communities, works have studied its ability to make a correct choice [7,19] as well as how best to collect and aggregate agents' delegation preferences [11,14,26]. It was implemented internally at Google [17], by Germany's Pirate Party [20], and in several other cases [24].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Characterizing Properties and Trade-offs of Centralized Delegation Mechanisms in Liquid Democracy

Brubach

Ballarin

Nazeer

2022

2022 ACM Conference on Fairness, Accountability, and Transparency

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Liquid democracy is a form of transitive delegative democracy that has received a flurry of scholarly attention from the computer science community in recent years. In its simplest form, every agent starts with one vote and may have other votes assigned to them via delegation from other agents. They can choose to delegate all votes assigned to them to another agent or vote directly with all votes assigned to them. However, many proposed realizations of liquid democracy allow for agents to express their delegation/voting preferences in more complex ways (e.g., a ranked list of potential delegates) and employ a centralized delegation mechanism to compute the final vote tally. In doing so, centralized delegation mechanisms can make decisions that affect the outcome of a vote and where/whether agents are able to delegate their votes. Much of the analysis thus far has focused on the ability of these mechanisms to make a correct choice. We extend this analysis by introducing and formalizing other important properties of a centralized delegation mechanism in liquid democracy with respect to crucial features such as accountability, transparency, explainability, fairness, and user agency. In addition, we evaluate existing methods in terms of these properties, show how some prior work can be augmented to achieve desirable properties, prove impossibility results for achieving certain sets of properties simultaneously, and highlight directions for future work. CCS CONCEPTS• Applied computing → Voting / election technologies; Egovernment; • Theory of computation → Algorithmic game theory and mechanism design.

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Liquid Democracy: An Algorithmic Perspective

Cited by 37 publications

References 11 publications

How Many Representatives Do We Need? The Optimal Size of a Congress Voting on Binary Issues

How Many Representatives Do We Need? The Optimal Size of a Congress Voting on Binary Issues

Liquid Democracy with Ranked Delegations

Characterizing Properties and Trade-offs of Centralized Delegation Mechanisms in Liquid Democracy

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