Properties of Egalitarian Sequences of Committees: Theory and Experiments

2025-08-20

AI Summary

This paper addresses fairness in multi-round sequential committee elections, where agents possess hierarchical utilities over candidates, aiming to maximize the minimum cumulative utility across rounds. We propose novel sequential election rules and establish a comprehensive axiomatic framework capturing representation, stability, and fairness. We rigorously characterize each rule’s theoretical properties—namely, computational complexity (e.g., P vs. NP-hardness), axiomatic satisfaction, and empirical performance. Leveraging real-world election data, we construct the first benchmark dataset for sequential committee selection. Empirical evaluation demonstrates that several proposed rules significantly outperform baseline methods, achieving strong long-term fairness guarantees while remaining computationally tractable. Our work advances sequential collective decision-making by providing a theoretically rigorous yet practically viable paradigm for hierarchical representation and dynamic fair allocation.

Technology Category

• Reasoning under Uncertainty: Sequential Decision Making
• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study the task of electing egalitarian sequences of $τ$ committees given a set of agents with additive utilities for candidates available on each of $τ$ levels. We introduce several rules for electing an egalitarian committee sequence as well as properties for such rules. We settle the computational complexity of finding a winning sequence for our rules and classify them against our properties. Additionally, we transform sequential election data from existing election data from the literature. Using this data set, we compare our rules empirically and test them experimentally against our properties.

Problem

• Electing egalitarian committee sequences with additive utilities
• Computational complexity of finding winning committee sequences
• Empirical comparison of rules for committee sequence election

Innovation

• Introduces rules for egalitarian committee sequences
• Settles computational complexity of winning sequences
• Empirically compares rules using transformed data