This paper bridges two perspectives: it studies the multi-secretary problem through the fairness lens of social choice, and examines multi-winner elections from the viewpoint of online decision making. After identifying the limitations of the prominent proportionality notion of Extended Justified Representation (EJR) in the online domain, the work proposes a set of mechanisms that merge techniques from online algorithms with rules from social choice -- such as the Method of Equal Shares and the Nash Rule -- and supports them through both theoretical analysis and extensive experimental evaluation.

We study voting rules for participatory budgeting, where a group of voters collectively decides which projects should be funded using a common budget.

We study voting rules for participatory budgeting, where a group of voters collectively decides which projects should be funded using a common budget.

Democratic processes increasingly aim to integrate large-scale voting with face-to-face deliberation, addressing the challenge of reconciling individual preferences with collective decision-making. This work introduces new methods that use algorithms and computational tools to bridge online voting with face-to-face deliberation, tested in two real-world scenarios: Kultur Komitee 2024 (KK24) and vTaiwan. These case studies highlight the practical applications and impacts of the proposed methods. We present three key contributions: (1) Radial Clustering for Preference Based Subgroups, which enables both in-depth and broad discussions in deliberative settings by computing homogeneous and heterogeneous group compositions with balanced and adjustable group sizes; (2) Human-in-the-loop MES, a practical method that enhances the Method of Equal Shares (MES) algorithm with real-time digital feedback. This builds algorithmic trust by giving participants full control over how much decision-making is delegated to the voting aggregation algorithm as compared to deliberation; and (3) the ReadTheRoom deliberation method, which uses opinion space mapping to identify agreement and divergence, along with spectrum-based preference visualisation to track opinion shifts during deliberation. This approach enhances transparency by clarifying collective sentiment and fosters collaboration by encouraging participants to engage constructively with differing perspectives. By introducing these actionable frameworks, this research extends in-person deliberation with scalable digital methods that address the complexities of modern decision-making in participatory processes.

Consider the problem of selecting a fixed number of k nodes from a network. Our goal is twofold: to identify the most influential nodes, and to ensure that the selection proportionally represents the diversity within the network. For instance, consider a network composed of three groups of densely connected nodes. Assume the groups contain 50%, 30%, and 20% of all nodes, respectively, and connections between groups are relatively sparse. If the objective is to select k = 10 nodes, a proportional approach would involve selecting five most influential nodes from the first group, three from the second, and two from the third group.

In participatory budgeting (PB), voters decide through voting which subset of projects to fund within a given budget. Proportionality in the context of PB is crucial to ensure equal treatment of all groups of voters. However, pure proportional rules can sometimes lead to suboptimal outcomes. We introduce the Method of Equal Shares with Bounded Overspending (BOS Equal Shares), a robust variant of Equal Shares that balances proportionality and efficiency. BOS Equal Shares addresses inefficiencies inherent in strict proportionality guarantees yet still provides good proportionality similar to the original Method of Equal Shares. In the course of the analysis, we also discuss a fractional variant of the method which allows for partial funding of projects.

Multiplayer games, when the number of players exceeds two, present unique challenges that fundamentally distinguish them from the extensively studied two-player zero-sum games. These challenges arise from the non-uniqueness of equilibria and the risk of agents performing highly suboptimally when adopting equilibrium strategies. While a line of recent works developed learning systems successfully achieving human-level or even superhuman performance in popular multiplayer games such as Mahjong, Poker, and Diplomacy, two critical questions remain unaddressed: (1) What is the correct solution concept that AI agents should find? and (2) What is the general algorithmic framework that provably solves all games within this class? This paper takes the first step towards solving these unique challenges of multiplayer games by provably addressing both questions in multiplayer symmetric normal-form games. We also demonstrate that many meta-algorithms developed in prior practical systems for multiplayer games can fail to achieve even the basic goal of obtaining agent's equal share of the total reward.

Scaling up deliberative and voting participation is a longstanding endeavor -- a cornerstone for direct democracy and legitimate collective choice. Recent breakthroughs in generative artificial intelligence (AI) and large language models (LLMs) provide unprecedented opportunities, but also alerting risks for digital democracy. AI personal assistants can overcome cognitive bandwidth limitations of humans, providing decision support capabilities or even direct AI representation of human voters at large scale. However, the quality of this representation and what underlying biases manifest when delegating collective decision making to LLMs is an alarming and timely challenge to tackle. By rigorously emulating with high realism more than >50K LLM voting personas in 81 real-world voting elections, we show that different LLMs (GPT 3, GPT 3.5, and Llama2) come with biases and significant inconsistencies in complex preferential ballot formats, compared to simpler and more consistent majoritarian elections. Strikingly, fair voting aggregation methods, such as equal shares, prove to be a win-win: fairer voting outcomes for humans with fairer AI representation. This novel underlying relationship proves paramount for democratic resilience in progressives scenarios with low voters turnout and voter fatigue supported by AI representatives: abstained voters are mitigated by recovering highly representative voting outcomes that are fairer. These insights provide remarkable foundations for science, policymakers and citizens in explaining and mitigating AI risks in democratic innovations.

Participatory budgeting, as a paradigm for democratic innovations, engages citizens in the distribution of a public budget to projects, which they propose and vote for implementation. So far, voting algorithms have been devised and studied in social choice literature to elect projects that are popular, while others prioritize on a proportional representation of voters' preferences, for instance, equal shares. However, the anticipated impact and novelty in the broader society by the winning projects, as selected by different algorithms, remains totally under-explored, lacking both a universal theory of impact for voting and a rigorous framework for impact and novelty assessments. This papers tackles this grand challenge towards new axiomatic foundations for designing effective and fair voting methods. This is via new and striking insights derived from a large-scale analysis of biases over 345 real-world voting outcomes, characterized for the first time by a novel portfolio of impact and novelty metrics. We find strong causal evidence that equal shares comes with impact loss in several infrastructural projects of different cost levels that have been so far over-represented. However, it also comes with a novel, yet over-represented, impact gain in welfare, education and culture. We discuss broader implications of these results and how impact loss can be mitigated at the stage of campaign design and project ideation.

The notion reflects an interest in bias-free decision making or, when protected classes of individuals are involved, in avoiding disparate impact to legally protected classes.3