Expected Frequency Matrices of Elections: Computation, Geometry, and Preference Learning
This work addresses the challenge of modeling and understanding voter preferences in computational social choice, but it is incremental as it builds on existing methods.
The paper tackles the problem of analyzing and learning real-world preference distributions in elections by computing frequency matrices for known vote distributions, and it results in a general framework for preference learning using these matrices.
We use the ``map of elections'' approach of Szufa et al. (AAMAS-2020) to analyze several well-known vote distributions. For each of them, we give an explicit formula or an efficient algorithm for computing its frequency matrix, which captures the probability that a given candidate appears in a given position in a sampled vote. We use these matrices to draw the ``skeleton map'' of distributions, evaluate its robustness, and analyze its properties. Finally, we develop a general and unified framework for learning the distribution of real-world preferences using the frequency matrices of established vote distributions.