Unveiling the Truth in Liquid Democracy with Misinformed Voters

Abstract

Liquid democracy is a voting paradigm that allows voters that are part of a social network to either vote directly or delegate their voting rights to one of their neighbors. The delegations are transitive in the sense, that a voter who decides to delegate, delegates both her own vote and the ones she has received through delegations. The additional exibility of the paradigm allows to transfer voting power towards a subset of voters ideally containing the most expert voters on the question at hand. It is thus tempting to assume that liquid democracy can lead to more accurate decisions. This claim has been investigated recently, maybe most importantly, by Kahng, Mackenzie, and Procaccia [30] and Caragiannis and Micha [10], who provide however mostly negative results using a model similar to the uncertain dichotomous choice model.In this paper, we provide new insights on this question. In particular, we investigate the so-called ODP-problem that has been formulated by Caragiannis and Micha [10]. Here, we are in a setting with two election alternatives out of which one is assumed to be correct. In ODP, the goal is to organise the delegations in the social network in order to maximize the probability that the correct alternative, referred to as ground truth, is elected. While the problem is known to be computationally hard, we strengthen existing hardness results by providing a novel strong approximation hardness result: For any positive constant 𝐶, we prove that, unless 𝑃 = 𝑁 𝑃, there is no polynomial-time algorithm for ODP that achieves an approximation guarantee of 𝛼 ≥ (ln 𝑛) −𝐶 , where 𝑛 is the number of voters. The reduction designed for this result uses poorly connected social networks in which some voters su er from misinformation. Interestingly, under some hypothesis on either the accuracies of voters or the connectivity of the network, we obtain a polynomial-time 1/2-approximation algorithm. This observation proves formally that the connectivity of the social network is a key feature for the e ciency of the liquid democracy paradigm. Lastly, we run extensive simulations and observe that simple algorithms (working either in a centralized or decentralized way) outperform direct democracy on a large class of instances. Overall, our contributions yield new insights on the question in which situations liquid democracy can be bene cial.

Unravelling Expressive Delegations: Complexity and Normative Analysis

“…There is also a substantial body of work on liquid democracy in the setting with ground truth (Kahng, Mackenzie, and Procaccia 2021;Gölz et al 2021;Caragiannis and Micha 2019;Becker et al 2021;Alouf-Heffetz et al 2022), as well as on game-theoretic aspects of delegation (Bloembergen, Grossi, and Lackner 2019;Escoffier, Gilbert, and Pass-Lanneau 2020;Zhang and Grossi 2021).…”

Towards Group Learning: Distributed Weighting of Experts

“…Our approach of decentralizing the weighting of experts is inspired by work in "wisdom of the crowds" and crowdsourcing [9,35], proxy voting [1] and truth-tracking in Liquid Democracy [5,6,39]. 1 For human agents, it is often more natural for them to assign weights or scores to the experts rather than to report probabilities as estimates of the experts' competences.…”

Towards a More Burkean Approach to Computational Social Choice

“…This results in an election in which only a subset of voters participate, each with a different weight (depending on the number of voters who have -directly or through others -given each agent their votes). There have been several papers discussing various aspects and variations of the model (Brill 2019;Brill and Talmon 2018;Zhang and Grossi 2021), and while Kahng, Mackenzie, and Procaccia (2021) (later strengthened by Caragiannis and Micha ( 2019)) raised the issue of too high concentration of power, several responses have been authored to tackle these issues, among other topics (Gölz et al 2021;Bloembergen, Grossi, and Lackner 2019;Abramowitz and Mattei 2019;Colley, Grandi, and Novaro 2021;Becker et al 2021).…”