Distribution Aggregation via Continuous Thiele's Rules
<|reference_start|>Distribution Aggregation via Continuous Thiele's Rules: We introduce the class of \textit{Continuous Thiele's Rules} that generalize the familiar \textbf{Thiele's rules} \cite{janson2018phragmens} of multi-winner voting to distribution aggregation problems. Each rule in that class maximizes $\sum_if(\pi^i)$ where $\pi^i$ is an agent $i$'s satisfaction and $f$ could be any twice differentiable, increasing and concave real function. Based on a single quantity we call the \textit{'Inequality Aversion'} of $f$ (elsewhere known as "Relative Risk Aversion"), we derive bounds on the Egalitarian loss, welfare loss and the approximation of \textit{Average Fair Share}, leading to a quantifiable, continuous presentation of their inevitable trade-offs. In particular, we show that the Nash Product Rule satisfies\textit{ Average Fair Share} in our setting.<|reference_end|>
@article{wagner2024distribution,
    title={Distribution Aggregation via Continuous Thiele's Rules},
    author={Jonathan Wagner and Reshef Meir},
    journal={arXiv preprint arXiv:2408.01054},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.01054},
    primaryClass={cs.GT}
}