Impartial Selection with Additive Guarantees via Iterated Deletion
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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+κ)/2) in a setting with n individuals where each individual casts O(n^κ) nominations, where κ∈[0,1]. For κ=0, i.e. when each individual casts at most a constant number of nominations, this bound is O(√(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.
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