Impartial Selection with Additive Guarantees via Iterated Deletion
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866910632735932416 |
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| author | Cembrano, Javier Fischer, Felix Hannon, David Klimm, Max |
| author_facet | Cembrano, Javier Fischer, Felix Hannon, David Klimm, Max |
| contents | Impartial selection is the selection of an individual from a group based on nominations by other members of the group, in such a way that individuals cannot influence their own chance of selection. For this problem, we give a deterministic mechanism with an additive performance guarantee of $O(n^{(1+κ)/2})$ in a setting with $n$ individuals where each individual casts $O(n^κ)$ nominations, where $κ\in[0,1]$. For $κ=0$, i.e., when each individual casts at most a constant number of nominations, this bound is $O(\sqrt{n})$. This matches the best-known guarantee for randomized mechanisms and a single nomination. For $κ=1$ the bound is $O(n)$. This is trivial, as even a mechanism that never selects provides an additive guarantee of $n-1$. We show, however, that it is also best possible: for every deterministic impartial mechanism there exists a situation in which some individual is nominated by every other individual and the mechanism either does not select or selects an individual not nominated by anyone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_08979 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Impartial Selection with Additive Guarantees via Iterated Deletion Cembrano, Javier Fischer, Felix Hannon, David Klimm, Max Computer Science and Game Theory Impartial selection is the selection of an individual from a group based on nominations by other members of the group, in such a way that individuals cannot influence their own chance of selection. For this problem, we give a deterministic mechanism with an additive performance guarantee of $O(n^{(1+κ)/2})$ in a setting with $n$ individuals where each individual casts $O(n^κ)$ nominations, where $κ\in[0,1]$. For $κ=0$, i.e., when each individual casts at most a constant number of nominations, this bound is $O(\sqrt{n})$. This matches the best-known guarantee for randomized mechanisms and a single nomination. For $κ=1$ the bound is $O(n)$. This is trivial, as even a mechanism that never selects provides an additive guarantee of $n-1$. We show, however, that it is also best possible: for every deterministic impartial mechanism there exists a situation in which some individual is nominated by every other individual and the mechanism either does not select or selects an individual not nominated by anyone. |
| title | Impartial Selection with Additive Guarantees via Iterated Deletion |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2205.08979 |