Bayesian Estimators As Voting Rules

Lirong Xia
Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, PMLR R14:672-681, 2016.

Abstract

We investigate the fairness of Bayesian estimators (BEs) by viewing them as (irresolute) voting rules and evaluating them by satisfaction of desirable social choice axioms. We characterize the class of BEs that satisfy neutrality by the class of BEs with neutral structures. We prove that a BE with a neutral structure is a minimax rule if it further satisfies parameter connectivity. We prove that no BE satisfies strict Condorcet criterion. We also propose three new BEs of natural frameworks and investigate their computational complexity and satisfaction of monotonicity and Condorcet criterion.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR14-xia16a, title = {{B}ayesian Estimators As Voting Rules}, author = {Xia, Lirong}, booktitle = {Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence}, pages = {672--681}, year = {2016}, editor = {Ihler, Alexander and Janzing, Dominik}, volume = {R14}, series = {Proceedings of Machine Learning Research}, month = {25--29 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r14/main/assets/xia16a/xia16a.pdf}, url = {https://proceedings.mlr.press/r14/xia16a.html}, abstract = {We investigate the fairness of Bayesian estimators (BEs) by viewing them as (irresolute) voting rules and evaluating them by satisfaction of desirable social choice axioms. We characterize the class of BEs that satisfy neutrality by the class of BEs with neutral structures. We prove that a BE with a neutral structure is a minimax rule if it further satisfies parameter connectivity. We prove that no BE satisfies strict Condorcet criterion. We also propose three new BEs of natural frameworks and investigate their computational complexity and satisfaction of monotonicity and Condorcet criterion.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Bayesian Estimators As Voting Rules %A Lirong Xia %B Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2016 %E Alexander Ihler %E Dominik Janzing %F pmlr-vR14-xia16a %I PMLR %P 672--681 %U https://proceedings.mlr.press/r14/xia16a.html %V R14 %X We investigate the fairness of Bayesian estimators (BEs) by viewing them as (irresolute) voting rules and evaluating them by satisfaction of desirable social choice axioms. We characterize the class of BEs that satisfy neutrality by the class of BEs with neutral structures. We prove that a BE with a neutral structure is a minimax rule if it further satisfies parameter connectivity. We prove that no BE satisfies strict Condorcet criterion. We also propose three new BEs of natural frameworks and investigate their computational complexity and satisfaction of monotonicity and Condorcet criterion. %Z Reissued by PMLR on 04 October 2026.
APA
Xia, L.. (2016). Bayesian Estimators As Voting Rules. Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R14:672-681 Available from https://proceedings.mlr.press/r14/xia16a.html. Reissued by PMLR on 04 October 2026.

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