Impartial Selection with Additive Guarantees via Iterated Deletion (Javier Cembrano, Felix A. Fischer, David Hannon and Max Klimm)
EC 2022 – Proc. 23rd ACM Conference on Economics and Computation, pp. 1104–1105.
@inproceedings{CembranoFischerHannon+2022,
author = {Javier Cembrano and Felix A. Fischer and David Hannon and Max Klimm},
booktitle = {EC 2022 – Proc. 23rd ACM Conference on Economics and Computation},
doi = {10.1145/3490486.3538294},
pages = {1104--1105},
title = {Impartial Selection with Additive Guarantees via Iterated Deletion},
year = {2022},
}
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. We give a deterministic mechanism with an additive performance guarantee of $\mathcal{O}(n^{(1+\kappa)/2})$ in a setting with $n$ individuals where each individual casts $\mathcal{O}(n^\kappa)$ nominations, where $\kappa \in [0,1]$. For $\kappa =0$, i.e. when each individual casts at most a constant number of nominations, this bound is $\mathcal{O}(\sqrt{n})$. This matches the best-known guarantee for randomized mechanisms and a single nomination. For $\kappa=1$ the bound is $\mathcal{O}(n)$. 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.
Optimal Impartial Correspondences (Javier Cembrano, Felix A. Fischer and Max Klimm)
WINE 2022 – Proc. 18th Conference on Web and Internet Economics, pp. 187–203.
@inproceedings{CembranoFischerKlimm2022,
author = {Javier Cembrano and Felix A. Fischer and Max Klimm},
booktitle = {WINE 2022 – Proc. 18th Conference on Web and Internet Economics},
title = {Optimal Impartial Correspondences},
year = {2022},
accepted = {07.09.2022},
doi = {10.1007/978-3-031-22832-2_11},
pages = {187--203},
}
We study mechanisms that select a subset of the vertex set of a directed graph in order to maximize the minimum indegree of any selected vertex, subject to an impartiality constraint that the selection of a particular vertex is independent of the outgoing edges of that vertex. For graphs with maximum outdegree $d$, we give a mechanism that selects at most $d+1$ vertices and only selects vertices whose indegree is at least the maximum indegree in the graph minus one. We then show that this is best possible in the sense that no impartial mechanism can only select vertices with maximum degree, even without any restriction on the number of selected vertices. We finally obtain the following trade-off between the maximum number of vertices selected and the minimum indegree of any selected vertex: when selecting at most $k$ of vertices out of $n$, it is possible to only select vertices whose indegree is at least the maximum indegree minus $\lfloor(n-2)/(k-1)\rfloor+1$.
