Expected Frequency Matrices of Elections: Computation, Geometry, and Preference Learning

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.