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Deterministic Impartial Selection with Weights
In the impartial selection problem, a subset of agents up to a fixed size
among a group of is to be chosen based on votes cast by the agents
themselves. A selection mechanism is impartial if no agent can influence its
own chance of being selected by changing its vote. It is -optimal if,
for every instance, the ratio between the votes received by the selected subset
is at least a fraction of of the votes received by the subset of size
with the highest number of votes. We study deterministic impartial
mechanisms in a more general setting with arbitrarily weighted votes and
provide the first approximation guarantee, roughly . When
the number of agents to select is large enough compared to the total number of
agents, this yields an improvement on the previously best known approximation
ratio of for the unweighted setting. We further show that our mechanism
can be adapted to the impartial assignment problem, in which multiple sets of
up to agents are to be selected, with a loss in the approximation ratio of
.Comment: To appear in the Proceedings of the 19th Conference on Web and
Internet Economics (WINE 2023
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