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

Niclas Boehmer; Robert Bredereck; Edith Elkind; Piotr Faliszewski; Stanisław Szufa

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

Niclas Boehmer, Robert Bredereck, Edith Elkind, Piotr Faliszewski, Stanisław Szufa

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

5 Scopus citations

Abstract

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.

Original language	English (US)
Title of host publication	Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
Editors	S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh
Publisher	Neural information processing systems foundation
ISBN (Electronic)	9781713871088
State	Published - 2022
Event	36th Conference on Neural Information Processing Systems, NeurIPS 2022 - New Orleans, United States Duration: Nov 28 2022 → Dec 9 2022

Publication series

Name	Advances in Neural Information Processing Systems
Volume	35
ISSN (Print)	1049-5258

Conference

Conference	36th Conference on Neural Information Processing Systems, NeurIPS 2022
Country/Territory	United States
City	New Orleans
Period	11/28/22 → 12/9/22

Funding

NB was supported by the DFG project MaMu (NI 369/19) and by the DFG project ComSoc-MPMS (NI 369/22). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 101002854). NB was supported by the DFG project MaMu (NI 369/19) and by the DFG project ComSoc-MPMS (NI 369/22). This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 101002854).

ASJC Scopus subject areas

Computer Networks and Communications
Information Systems
Signal Processing

Cite this

Boehmer, N., Bredereck, R., Elkind, E., Faliszewski, P., & Szufa, S. (2022). Expected Frequency Matrices of Elections: Computation, Geometry, and Preference Learning. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, & A. Oh (Eds.), Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022 (Advances in Neural Information Processing Systems; Vol. 35). Neural information processing systems foundation.

Boehmer, Niclas ; Bredereck, Robert ; Elkind, Edith et al. / Expected Frequency Matrices of Elections : Computation, Geometry, and Preference Learning. Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022. editor / S. Koyejo ; S. Mohamed ; A. Agarwal ; D. Belgrave ; K. Cho ; A. Oh. Neural information processing systems foundation, 2022. (Advances in Neural Information Processing Systems).

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abstract = "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.",

author = "Niclas Boehmer and Robert Bredereck and Edith Elkind and Piotr Faliszewski and Stanis{\l}aw Szufa",

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Boehmer, N, Bredereck, R, Elkind, E, Faliszewski, P & Szufa, S 2022, Expected Frequency Matrices of Elections: Computation, Geometry, and Preference Learning. in S Koyejo, S Mohamed, A Agarwal, D Belgrave, K Cho & A Oh (eds), Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022. Advances in Neural Information Processing Systems, vol. 35, Neural information processing systems foundation, 36th Conference on Neural Information Processing Systems, NeurIPS 2022, New Orleans, United States, 11/28/22.

Expected Frequency Matrices of Elections: Computation, Geometry, and Preference Learning. / Boehmer, Niclas; Bredereck, Robert; Elkind, Edith et al.
Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022. ed. / S. Koyejo; S. Mohamed; A. Agarwal; D. Belgrave; K. Cho; A. Oh. Neural information processing systems foundation, 2022. (Advances in Neural Information Processing Systems; Vol. 35).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AB - 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.

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Boehmer N, Bredereck R, Elkind E, Faliszewski P, Szufa S. Expected Frequency Matrices of Elections: Computation, Geometry, and Preference Learning. In Koyejo S, Mohamed S, Agarwal A, Belgrave D, Cho K, Oh A, editors, Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022. Neural information processing systems foundation. 2022. (Advances in Neural Information Processing Systems).

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

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