Deterministic Impartial Selection with Weights (Javier Cembrano, Svenja M. Griesbach, and Maximilian J. Stahlberg)
ACM Transactions on Economics and Computation, 12(3):10:1–10:22, 2024.
@article{CembranoGriesbachStahlberg2024,
author = {Javier Cembrano and Svenja M. Griesbach and Maximilian J. Stahlberg},
title = {Deterministic Impartial Selection with Weights},
journal = {ACM Transactions on Economics and Computation},
year = {2024},
volume = {12},
number = {3},
pages = {10:1--10:22},
doi = {10.1145/3677177},
arxiv = {2310.14991},
}
In the impartial selection problem, a subset of agents up to a fixed size $k$ among a group of $n$ is to be chosen based on votes cast by the agents themselves. A selection mechanism is \emphimpartial if no agent can influence its own chance of being selected by changing its vote. It is \emph$\alpha$-optimal if, for every instance, the ratio between the votes received by the selected subset is at least a fraction of $\alpha$ of the votes received by the subset of size $k$ 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 $1/\lceil 2n/k\rceil$. 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 $1/k$ 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 $k$ agents are to be selected, with a loss in the approximation ratio of $1/2$.