Impartial Selection with Additive Guarantees via Iterated Deletion.

Abstract: 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 $O(n^{(1+\gamma)/2})$ in a setting with $n$ individuals where each individual casts $O(n^{\gamma})$ nominations, where $\gamma \in [0,1]$. For $\gamma=0$, 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 $\gamma=1$ 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.

Posted on Nov 21, 2022 in ACGO, Seminars