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1. Anonymous and Copy-Robust Delegations for Liquid Democracy

   Utke, Markus; Schmidt-Kraepelin, Ulrike (January 2023, Advances in neural information processing systems)

   Oh, A; Naumann, T; Globerson, A; Saenko, K; Hardt, M; Levine, S (Ed.)

   Liquid democracy with ranked delegations is a novel voting scheme that unites the practicability of representative democracy with the idealistic appeal of direct democracy: Every voter decides between casting their vote on a question at hand or delegating their voting weight to some other, trusted agent. Delegations are transitive, and since voters may end up in a delegation cycle, they are encouraged to indicate not only a single delegate, but a set of potential delegates and a ranking among them. Based on the delegation preferences of all voters, a delegation rule selects one representative per voter. Previous work has revealed a trade-off between two properties of delegation rules called anonymity and copy-robustness. To overcome this issue we study two fractional delegation rules: Mixed Borda branching, which generalizes a rule satisfying copy-robustness, and the random walk rule, which satisfies anonymity. Using the Markov chain tree theorem, we show that the two rules are in fact equivalent, and simultaneously satisfy generalized versions of the two properties. Combining the same theorem with Fulkerson's algorithm, we develop a polynomial-time algorithm for computing the outcome of the studied delegation rule. This algorithm is of independent interest, having applications in semi-supervised learning and graph theory. 

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2. In defense of liquid democracy

   Daniel Halpern; Joseph Y. Halpern, Ali Jadbabaie; Elchanan Mossel; Ariel Procaccia; Manon Revel (July 2023, Twenty-fourth ACM Conference on Electronic Commerce)

   \ (Ed.)

   Fluid (or liquid) democracy is a voting paradigm that allows voters to choose between directly voting and transitively delegating their votes to other voters. While fluid democracy has been viewed as a system that can combine the best aspects of direct and representative democracy, it can also result in situations where few voters amass a large amount of influence. To analyze the impact of this shortcoming, we consider what has been called an epistemic setting, where voters decide on a binary issue for which there is a ground truth. Previous work has shown that under certain assumptions on the delegation mechanism, the concentration of power is so severe that fluid democracy is less likely to identify the ground truth than direct voting. We examine different, arguably more realistic, classes of mechanisms, and prove they behave well by ensuring that (with high probability) there is a limit on concentration of power. Our proofs demonstrate that delegations can be treated as stochastic processes and that they can be compared to well-known processes from the literature — such as preferential attachment and multi-types branching process—that are sufficiently bounded for our purposes. Our results suggest that the concerns raised about fluid democracy can be overcome, thereby bolstering the case for this emerging paradigm. 

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3. Pandering in a (flexible) representative democracy

   Sun, Xiaolin; Masur, Jacob; Abramowitz, Ben; Mattei, Nicholas; Zheng, Zizhan (August 2023, Proceedings of the 39th Conference on Uncertainty in Artificial Intelligence)

   In representative democracies, regular election cycles are supposed to prevent misbehavior by elected officials, hold them accountable, and subject them to the “will of the people." Pandering, or dishonest preference reporting by candidates campaigning for election, undermines this democratic idea. Much of the work on Computational Social Choice to date has investigated strategic actions in only a single election. We introduce a novel formal model of pandering and examine the resilience of two voting systems, Representative Democracy (RD) and Flexible Representative Democracy (FRD), to pandering within a single election and across multiple rounds of elections. For both voting systems, our analysis centers on the types of strategies candidates employ and how voters update their views of candidates based on how the candidates have pandered in the past. We provide theoretical results on the complexity of pandering in our setting for a single election, formulate our problem for multiple cycles as a Markov Decision Process, and use reinforcement learning to study the effects of pandering by single candidates and groups of candidates over many rounds. 

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4. Liquid Democracy: An Algorithmic Perspective

   https://doi.org/10.1613/jair.1.12261  

   Kahng, Anson; Mackenzie, Simon; Procaccia, Ariel (January 2021, Journal of Artificial Intelligence Research)

   null (Ed.)

   We study liquid democracy, a collective decision making paradigm that allows voters to transitively delegate their votes, through an algorithmic lens. In our model, there are two alternatives, one correct and one incorrect, and we are interested in the probability that the majority opinion is correct. Our main question is whether there exist delegation mechanisms that are guaranteed to outperform direct voting, in the sense of being always at least as likely, and sometimes more likely, to make a correct decision. Even though we assume that voters can only delegate their votes to better-informed voters, we show that local delegation mechanisms, which only take the local neighborhood of each voter as input (and, arguably, capture the spirit of liquid democracy), cannot provide the foregoing guarantee. By contrast, we design a non-local delegation mechanism that does provably outperform direct voting under mild assumptions about voters. 

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5. Statement Voting

   https://doi.org/10.1007/978-3-030-32101-7_38  

   Zhang, Bingsheng; Zhou, Hong-Sheng (September 2019, Lecture notes in computer science)

   The conventional (election) voting systems, e.g., representative democracy, have many limitations and often fail to serve the best interest of the people in a collective decision-making process. To address this issue, the concept of liquid democracy has been emerging as an alternative decision-making model to make better use of “the wisdom of crowds”. However, there is no known cryptographically secure e-voting implementation that supports liquid democracy. In this work, we propose a new voting concept called statement voting, which can be viewed as a natural extension of the conventional voting approaches. In the statement voting, instead of defining a concrete elec- tion candidate, each voter can define a statement in his/her ballot but leave the vote “undefined” during the voting phase. During the tally phase, the (conditional) actions expressed in the statement will be carried out to determine the final vote. We initiate the study of statement voting under the Universal Composability (UC) framework, and propose several construction frameworks together with their instantiations. As an application, we show how statement voting can be used to realize a UC-secure liquid democracy voting system. We remark that our statement voting can be extended to enable more complex voting and generic ledger-based non-interactive multi-party computation. We believe that the statement voting concept opens a door for constructing a new class of e-voting schemes. 

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