Aggregating Preferences Over the Simplex

• Applicant: Professor Dr. Felix Brandt
• Subject Area: Theoretical Computer Science ; Methods in Artificial Intelligence and Machine Learning
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 562936782

This project studies the aggregation of preferences over points within the k-dimensional simplex. These points can be interpreted as distributions of a divisible and homogeneous resource—such as money, probability, time, or space—across k+1 projects of public interest. The goal is to find mutually agreeable distributions based on the preferences of multiple agents. To model individual preferences, we will explore a wide range of utility functions over distributions, including linear utilities, Leontief utilities, Cobb-Douglas utilities, and disutility functions derived from norm-based distance measures. The results of this project will have immediate consequences in three trending subareas of computational social choice: randomized voting rules, budget aggregation, and donor coordination. These areas are tightly connected to real-world applications of increasing significance. Methodologically, the project will employ classical analytical techniques from mathematical disciplines such as linear algebra and convex geometry, as well as computer-aided techniques, including SAT solving and mixed integer programming.

• DFG Programme: Research Grants