Distribution Aggregation via Continuous Thiele's Rules
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914897630068736 |
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| author | Wagner, Jonathan Meir, Reshef |
| author_facet | Wagner, Jonathan Meir, Reshef |
| contents | 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 $\sum_if(π^i)$ where $π^i$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01054 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distribution Aggregation via Continuous Thiele's Rules Wagner, Jonathan Meir, Reshef Computer Science and Game Theory 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 $\sum_if(π^i)$ where $π^i$ 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. |
| title | Distribution Aggregation via Continuous Thiele's Rules |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2408.01054 |