Federated learning (FL) mechanisms typically require each client to transfer their weights to a central server, irrespective of how useful they are. In order to avoid wasteful data transfer costs from clients to the central server, we propose the use of consensus based protocols to identify a subset of clients with most useful model weights at each data transfer step. First, we explore the application of existing fluid democracy protocols to FL from a performance standpoint, comparing them with traditional one-person-one-vote (also known as 1p1v or FedAvg). We propose a new fluid democracy protocol named viscous-retained democracy that always does better than 1p1v under the same assumptions as existing fluid democracy protocols while also not allowing for influence accumulation. Secondly, we identify weaknesses of fluid democracy protocols from an adversarial lens in terms of their dependence on topology and/ or number of adversaries required to negatively impact the global model weights. To this effect, we propose an algorithm (FedVRD) that dynamically limits the effect of adversaries while minimizing cost by leveraging the delegation topology.

Liquid democracy is a mechanism for the division of labor in decision-making through the transitive delegation of influence. In essence, all individuals possess the autonomy to determine the issues with which they will engage directly, while for other matters, they may appoint a representative of their choosing. So far, the literature has studied the delegation structures emerging in liquid democracy as static. As a result, transitivity defined as the capacity to transfer acquired authority to another entity, has been identified as a concern as it would be conducive to unrestrained accumulation of power. Focusing on the implementation of liquid democracy supported by the LiquidFeedback software, we propose a novel approach to assessing the influence of voting nodes in a transitive delegation graph, taking into account the process nature of real-world liquid democracy in which delegation and voting are distinct and increasingly independent activities. By introducing a novel model of delegations in liquid democracy, we show how transitivity may in fact contribute to an effective regulation of deliberation influence and decision-making power. While maintaining the one-person, one-vote paradigm for all votes cast, the anticipated influence of an agent, to the extent it is stemming from transitivity, experiences a precipitous decline following an exponential trajectory. In general, it is our objective to move the first steps towards a rigorous analysis of liquid democracy as an adaptive democratic representation process. The adaptivity aspect of liquid democracy has not yet been explored within the existing academic literature despite it being, we believe, one of its most important features. We therefore also outline a research agenda focusing on this aspect of liquid democracy.

We examine an approval-based model of Liquid Democracy with a budget constraint on voting and delegating costs, aiming to centrally select casting voters ensuring complete representation of the electorate. From a computational complexity perspective, we focus on minimizing overall costs, maintaining short delegation paths, and preventing excessive concentration of voting power. Furthermore, we explore computational aspects of strategic control, specifically, whether external agents can change election components to influence the voting power of certain voters.

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.

Analyzing social media trends can create a win-win situation for both creators and consumers. Creators can receive fair compensation, while consumers gain access to engaging, relevant, and personalized content. This paper proposes a new model for analyzing Bitcoin trends on Twitter by incorporating a 'liquid democracy' approach based on user reputation. This system aims to identify the most impactful trends and their influence on Bitcoin prices and trading volume. It uses a Twitter sentiment analysis model based on a reputation rating system to determine the impact on Bitcoin price change and traded volume. In addition, the reputation model considers the users' higher-order friends on the social network (the initial Twitter input channels in our case study) to improve the accuracy and diversity of the reputation results. We analyze Bitcoin-related news on Twitter to understand how trends and user sentiment, measured through our Liquid Rank Reputation System, affect Bitcoin price fluctuations and trading activity within the studied time frame. This reputation model can also be used as an additional layer in other trend and sentiment analysis models. The paper proposes the implementation, challenges, and future scope of the liquid rank reputation model.

In the past several years, the training of machine learning systems has consumed increasingly large amounts of data and compute. In the search for ever-improving performance, models have grown larger, more data has been collected, and the cost of machine learning has grown while performance only improves incrementally [16]. This leads to negative repercussions affecting privacy by incentivizing mass data collection, increased development time due to the time taken to train models, and significant environmental costs. It also limits access to the best-performing models to those groups with enough resources to support storing massive amounts of data and training large models. Recent advances have begun to consider learning from few examples for settings where data is hard to generate or resources are limited [21] however this field is still in its early stages. We propose adapting an existing paradigm of opinion aggregation to address the problem of compute requirements during classifier ensemble training. Ensemble learning for classification has long studied the problem of combining class predictions from groups of classifiers into a single output prediction. Condorcet's Jury Theorem, a well-known result from social choice theory (predating ML research by 2 centuries), states that if voters attempt to guess the correct outcome of some ground-truth decision then the majority vote is increasingly likely to be correct as voters are added if all voters are independent and have accuracy above 0.5

Liquid democracy is a hybrid direct-representative decision making process that provides each voter with the option of either voting directly or to delegate their vote to another voter, i.e., to a representative of their choice. One of the proposed advantages of liquid democracy is that, in general, it is assumed that voters will delegate their vote to others that are better informed, which leads to more informed and better decisions. Considering an audience from various knowledge domains, we provide an accessible high-level analysis of a prominent critique of liquid democracy by Caragiannis and Micha. Caragiannis and Micha's critique contains three central topics: 1. Analysis using their $\alpha$-delegation model, which does not assume delegation to the more informed; 2. Novel delegation network structures where it is advantageous to delegate to the less informed rather than the more informed; and 3. Due to NP hardness, the implied impracticability of a social network obtaining an optimal delegation structure. We show that in the real world, Caragiannis and Micha's critique of liquid democracy has little or no relevance. Respectively, our critique is based on: 1. The identification of incorrect $\alpha$-delegation model assumptions; 2. A lack of novel delegation structures and their effect in a real-world implementation of liquid democracy, which would be guaranteed with constraints that sensibly distribute voting power; and 3. The irrelevance of an optimal delegation structure if the correct result is guaranteed regardless. We conclude that Caragiannis and Micha's critique has no significant negative relevance to the proposition of liquid democracy.

In recent years, the study of various models and questions related to Liquid Democracy has been of growing interest among the community of Computational Social Choice. A concern that has been raised, is that current academic literature focuses solely on static inputs, concealing a key characteristic of Liquid Democracy: the right for a voter to change her mind as time goes by, regarding her options of whether to vote herself or delegate her vote to other participants, till the final voting deadline. In real life, a period of extended deliberation preceding the election-day motivates voters to adapt their behaviour over time, either based on observations of the remaining electorate or on information acquired for the topic at hand. By adding a temporal dimension to Liquid Democracy, such adaptations can increase the number of possible delegation paths and reduce the loss of votes due to delegation cycles or delegating paths towards abstaining agents, ultimately enhancing participation. Our work takes a first step to integrate a time horizon into decision-making problems in Liquid Democracy systems. Our approach, via a computational complexity analysis, exploits concepts and tools from temporal graph theory which turn out to be convenient for our framework.

Transitive proxy voting (or "liquid democracy") is a novel form of collective decision making, often framed as an attractive hybrid of direct and representative democracy. Although the ideas behind liquid democracy have garnered widespread support, there have been relatively few attempts to model it formally. This paper makes three main contributions. First, it proposes a new social choice-theoretic model of liquid democracy, which is distinguished by taking a richer formal perspective on the process by which a voter chooses a proxy. Second, it examines the model from an axiomatic perspective, proving (a) a proxy vote analogue of May's Theorem and (b) an impossibility result concerning monotonicity properties in a proxy vote setting. Third, it explores the topic of manipulation in transitive proxy votes. Two forms of manipulation specific to the proxy vote setting are defined, and it is shown that manipulation occurs in strictly more cases in proxy votes than in classical votes.

As the world's democratic institutions are challenged by dissatisfied citizens, political scientists and also computer scientists have proposed and analyzed various (innovative) methods to select representative bodies, a crucial task in every democracy. However, a unified framework to analyze and compare different selection mechanisms is missing, resulting in very few comparative works. To address this gap, we advocate employing concepts and tools from computational social choice in order to devise a model in which different selection mechanisms can be formalized. Such a model would allow for desirable representation axioms to be conceptualized and evaluated. We make the first step in this direction by proposing a unifying mathematical formulation of different selection mechanisms as well as various social-choice-inspired axioms such as proportionality and monotonicity.