2024/08/02 by Jonathan Wagner, Wagner, Jonathan, Reshef Meir +1 · 1 citation
Mathematics · #Advanced Statistical Methods and Models #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.2408.01054
openalex publication_date 2024/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the class of Continuous Thiele's Rules that generalize the familiar Thiele's rules \citejanson2018phragmens of multi-winner voting to distribution aggregation problems. Each rule in that class maximizes ∑if(πi) where πi 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 'Inequality Aversion' of f (elsewhere known as "Relative Risk Aversion"), we derive bounds on the Egalitarian loss, welfare loss and the approximation of Average Fair Share, leading to a quantifiable, continuous presentation of their inevitable trade-offs. In particular, we show that the Nash Product Rule satisfies Average Fair Share in our setting.