Methodology

Computational Social Choice

All of the methods used in this website belong to the field of Computational Social Choice (COMSOC). Broadly, computational social choice is concerned with the problem of aggregating heterogeneous information into a collective decision. The original motivation for COMSOC has been the aggregation of the (possibly conflicting) preferences of multiple agents into a joint decision. For example, this includes the study of voting problems (which candidate(s) should we choose given the preferences of the voters?), allocation problems (how should we allocate items to the agents based on their preferences?), and underlying communication issues (how should we elicit the preferences of the agents?). Moreover, the methods studied in this field have also proven valuable for more technical applications, such as rank aggregation and clustering. An excellent introduction to the field of COMSOC is provided by the Handbook of Computational Social Choice by Brandt et al.

The Rank Aggregation Framework

In rank aggregation, the problem is to combine multiple weighted input rankings over a set of candidates (e.g., cities or universities) into a single output ranking. For all our methods, it is important that each input ranking ranks all candidates and that no ties in the input or output rankings are permitted. Hence, the input for rank aggregation is a profile of input rankings $({\succ_1},\dots,{\succ_n})$ and their weights $(w_1,\dots,w_n)$. Throughout this website, we will denote by $m$ the number of candidates and by $n$ the number of input rankings in the considered instance. Finally, a rank aggregation method is a function that chooses for every profile of input rankings and their corresponding weights a single output ranking. In the COMSOC literature, these functions are often called social welfare functions or social preference functions. Subsequently, we discuss our 19 default methods as well as the customizations of these rules possible in the Customize your Rule tab.

Rank Aggregation Methods

References

• Aziz, H., & Lee, B. E. (2020). The expanding approvals rule: Improving proportional representation and monotonicity. Social Choice and Welfare, 54(1), pp. 1–45.
• Aziz, H., Lederer, P., Peters, D., Peters, J., & Ritossa, A. (2025). Committee monotonicity and proportional representation for ranked preferences. In Proceedings of the 26th ACM Conference on Economics and Computation, p. 896.
• Aziz, H., Lederer, P., & Sharara, M. Proportional rank aggregation with generalized Kemeny utilities. Working paper.
• Boehmer, N., Bredereck, R., & Peters, D. (2026). Rank aggregation using scoring rules. Theory and Decision. Online first.
• Brandt, F., Conitzer, V., Endriss, U., Lang, J., & Procaccia A. D. (Ed.). (2016). Handbook of Computational Social Choice. Cambridge University Press.
• Brandt, F. (2025). Social Choice Theory: A Modern Approach with Computational Aspects.
• Conitzer, V., Davenport, A., & Kalagnanam, J. (2006). Improved bounds for computing Kemeny rankings. In Proceedings of the 21st AAAI Conference on Artificial Intelligence, pp. 620–626.
• Faliszewski, P., Skowron, P., Slinko, A., & Talmon, N. (2017). Multiwinner voting: A new challenge for social choice theory. In U. Endriss (Ed.), Trends in Computational Social Choice, pp. 27–47. AI Access.
• Lederer, P. (2025). Proportional representation in rank aggregation. arXiv:2508.16177.
• Lederer, P., Peters, D., & Wąs, T. (2024). The squared Kemeny rule for averaging rankings. In Proceedings of the 25th ACM Conference on Economics and Computation, p. 755.