Majorized Bayesian Persuasion and Fair Selection
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910651615543296 |
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| author | Banerjee, Siddhartha Munagala, Kamesh Shen, Yiheng Wang, Kangning |
| author_facet | Banerjee, Siddhartha Munagala, Kamesh Shen, Yiheng Wang, Kangning |
| contents | We address the fundamental problem of selection under uncertainty by modeling it from the perspective of Bayesian persuasion. In our model, a decision maker with imperfect information always selects the option with the highest expected value. We seek to achieve fairness among the options by revealing additional information to the decision maker and hence influencing its subsequent selection. To measure fairness, we adopt the notion of majorization, aiming at simultaneously approximately maximizing all symmetric, monotone, concave functions over the utilities of the options. As our main result, we design a novel information revelation policy that achieves a logarithmic-approximation to majorization in polynomial time. On the other hand, no policy, regardless of its running time, can achieve a constant-approximation to majorization. Our work is the first non-trivial majorization result in the Bayesian persuasion literature with multi-dimensional information sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11798 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Majorized Bayesian Persuasion and Fair Selection Banerjee, Siddhartha Munagala, Kamesh Shen, Yiheng Wang, Kangning Computer Science and Game Theory We address the fundamental problem of selection under uncertainty by modeling it from the perspective of Bayesian persuasion. In our model, a decision maker with imperfect information always selects the option with the highest expected value. We seek to achieve fairness among the options by revealing additional information to the decision maker and hence influencing its subsequent selection. To measure fairness, we adopt the notion of majorization, aiming at simultaneously approximately maximizing all symmetric, monotone, concave functions over the utilities of the options. As our main result, we design a novel information revelation policy that achieves a logarithmic-approximation to majorization in polynomial time. On the other hand, no policy, regardless of its running time, can achieve a constant-approximation to majorization. Our work is the first non-trivial majorization result in the Bayesian persuasion literature with multi-dimensional information sets. |
| title | Majorized Bayesian Persuasion and Fair Selection |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2410.11798 |