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\title{Truthful Elicitation of Imprecise Forecasts}

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\begin{document}

\author[1]{Anurag Singh}
\author[2]{Siu Lun Chau}
\author[1]{Krikamol Muandet}
\affil[1]{%
    Rational Intelligence Lab, CISPA Helmholtz Center for Information Security, 
    Saarbr\"ucken, 
    Germany
}
\affil[2]{%
    College of Computing \& Data Science, Nanyang Technological University, Singapore
}
%\author[1]{\href{mailto:<jj@example.edu>?Subject=Your UAI 2025 paper}{Jane~J.~von~O'L\'opez}{}}
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\maketitle

\begin{abstract}
    The quality of probabilistic forecasts is crucial for decision-making under uncertainty. While proper scoring rules incentivize truthful reporting of precise forecasts, they fall short when forecasters face epistemic uncertainty about their beliefs, limiting their use in safety-critical domains where decision-makers~(DMs) prioritize proper uncertainty management. To address this, we propose a framework for scoring \emph{imprecise forecasts}---forecasts given as a set of beliefs. Despite existing impossibility results for deterministic scoring rules, we enable truthful elicitation by drawing connection to social choice theory and introducing a two-way communication framework where DMs first share their aggregation rules (e.g., averaging or min-max) used in downstream decisions for resolving forecast ambiguity. This, in turn, helps forecasters resolve indecision during elicitation. We further show that truthful elicitation of imprecise forecasts is achievable using proper scoring rules randomized over the aggregation procedure. Our approach allows DM to elicit and integrate the forecaster's epistemic uncertainty into their decision-making process, thus improving credibility.
\end{abstract}



% \begin{abstract}
%     The quality of probabilistic forecasts is crucial for decision-making under uncertainty. Although proper scoring rules incentivize truthful reporting of precise probabilistic forecasts, they fall short in scenarios where forecasters face epistemic uncertainty about their beliefs. This limitation restricts the applicability of such forecasts in safety-critical domains, where decision-makers (DMs) prioritize proper uncertainty management. To address this, we propose a general framework for scoring imprecise forecasts—forecasts represented as sets of beliefs. While existing impossibility results for deterministic scoring rules highlight challenges in eliciting truthful imprecise forecasts, we address this by introducing a two-way communication framework between DMs and forecasters. Specifically, the DM first communicates their choice of aggregation rules (e.g., averaging or min-max procedures) used in downstream decision-making. This helps the forecaster to resolve indecision due to imprecision during the elicitation process. Building on this framework, we further show that truthful elicitation of imprecise forecasts becomes possible while using a proper scoring rule randomized with respect to the aggregation procedure. Our approach effectively incorporates the epistemic uncertainty of the forecaster into the decision-making process, leading to more credible decisions.
% \end{abstract}




% \begin{abstract}
% The quality of probabilistic forecasts is essential for decision-making under uncertainty. While proper scoring rules can incentivize truthful reporting of precise probabilistic forecasts, their inability to cater for scenarios where the forecaster's epistemic uncertainty affects the downstream decision-making processes. This paper proposes a general framework for scoring imprecise forecasts. We build on classical proper scoring rules while addressing the inherent impossibility of strict properness for imprecise forecast elicitation. To overcome this impossibility, we introduce two-way communication between the decision-maker and the forecaster. Specifically, the decision-maker begins by communicating information about aggregation rules used for downstream decision-making to the forecaster. During elicitation, aggregation allows the forecaster to resolve the indecision caused by their epistemic uncertainty. We show that truthful elicitation of imprecise forecasts is possible when decision-makers share only a distribution over the plausible aggregations.
% \end{abstract}

\doparttoc % Tell to minitoc to generate a toc for the parts
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\input{uai2025/new_content/section-introduction}
\input{uai2025/new_content/section-preliminaries}
\input{uai2025/new_content/section-setup}
\input{uai2025/new_content/section-imprecisescoringrule}
\input{uai2025/new_content/section-aggregation}
\input{uai2025/new_content/section-randomizedtailorscoringrule}
\input{uai2025/new_content/related-work}
\input{uai2025/new_content/discussion}

\textbf{Acknowledgement}
We thank the anonymous reviewers for their insightful feedback.

\bibliography{refs,ref_alan,ref_krik,ref_krik_ext}

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\end{document}
