Aggregating Quantitative Relative Judgments: From Social Choice to Ranking Prediction (2410.05550v1)

Abstract: Quantitative Relative Judgment Aggregation (QRJA) is a new research topic in (computational) social choice. In the QRJA model, agents provide judgments on the relative quality of different candidates, and the goal is to aggregate these judgments across all agents. In this work, our main conceptual contribution is to explore the interplay between QRJA in a social choice context and its application to ranking prediction. We observe that in QRJA, judges do not have to be people with subjective opinions; for example, a race can be viewed as a "judgment" on the contestants' relative abilities. This allows us to aggregate results from multiple races to evaluate the contestants' true qualities. At a technical level, we introduce new aggregation rules for QRJA and study their structural and computational properties. We evaluate the proposed methods on data from various real races and show that QRJA-based methods offer effective and interpretable ranking predictions.

• The paper introduces new aggregation rules for QRJA, achieving almost-linear time algorithms for convex loss functions.
• The methodology bridges social choice theory with ranking prediction by leveraging real-world datasets like chess tournaments and marathons.
• The results underscore QRJA's interpretability and potential in enhancing AI systems, with implications for sports analytics and recommendation systems.

An Expert Overview of Quantitative Relative Judgment Aggregation (QRJA)

The paper "Aggregating Quantitative Relative Judgments: From Social Choice to Ranking Prediction" by Yixuan Even Xu, Hanrui Zhang, Yu Cheng, and Vincent Conitzer presents a comprehensive paper on Quantitative Relative Judgment Aggregation (QRJA). This topic bridges the disciplines of computational social choice and ranking prediction, providing novel insights into how relative judgments can be formalized and utilized in practice.

Conceptual Contributions

The primary conceptual contribution of this work is the exploration of QRJA within the context of social choice and its application to ranking prediction. The authors illustrate how judgments, such as race results indicating contestants' relative times, can be aggregated to evaluate contestants' true qualities. This perspective allows them to view QRJA not merely as opinions from judges but as direct measurements from events, creating a link between social choice theory and learning-to-rank problems.

Technical Advancements

The paper introduces new aggregation rules for QRJA and investigates their structural and computational properties. One of the key technical achievements is the development of almost-linear time algorithms for QRJA problems when the loss function is convex (i.e., $p \ge 1$). The computational complexity results are significant—showing that these problems are solvable in polynomial time for convex cases and establishing NP-hardness for non-convex cases ($p < 1$).

Empirical Evaluation

Empirically, the paper evaluates QRJA using real-world datasets, such as results from chess tournaments and marathons. The paper compares QRJA-based methods against benchmarks like matrix factorization, mean/median algorithms, and traditional social choice methods like the Borda Count. QRJA methods demonstrate strong performance, especially in terms of ordinal accuracy and quantitative predictions, highlighting their practical applicability in predicting contest results.

Implications and Future Directions

The implications of this research extend across both practical and theoretical realms. Practically, QRJA provides an interpretable method for ranking predictions, which is valuable in domains like sports analytics and recommendation systems. Theoretically, the connection forged between social choice and machine learning insights opens avenues for further exploration into how principles from one domain can enhance techniques in the other.

The paper also speculates on future developments in AI, such as building more efficient algorithms for various $p$ values in $\ell_p$ QRJA and experimenting with subsampling techniques to handle large datasets. These directions point to a richer integration of QRJA in diverse AI applications, potentially impacting how automated systems interact with human preferences and judgments.

Conclusion

This work provides valuable contributions to the intersection of social choice and ranking prediction, offering both theoretical depth and practical solutions. By extending the understanding of QRJA, it lays the groundwork for advancements in both AI system design and our broader understanding of aggregation in multi-agent settings. The authors' efforts in settling computational complexities and testing empirical performance signify a robust framework for future applications and research in this evolving area.