# Property Elicitation on Imprecise Probabilities

arXiv: https://arxiv.org/abs/2507.05857 · HTML: https://mlsanity.com/paper/2507.05857/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 31 references that are in the map.
- First posted on arXiv 8 Jul 2025.

## Builds on (most cited first, 5 of 5)

- [Distributionally Robust Optimization: A Review](https://mlsanity.com/paper/1908.05659/) (2019)
- [On-Demand Sampling: Learning Optimally from Multiple Distributions](https://mlsanity.com/paper/2210.12529/) (2022)
- [Scoring Rules and Calibration for Imprecise Probabilities](https://mlsanity.com/paper/2410.23001/) (2024)
- [Forecast Evaluation of Quantiles, Prediction Intervals, and other Set-Valued Functionals](https://mlsanity.com/paper/1910.07912/) (2019)
- [Truthful Elicitation of Imprecise Forecasts](https://mlsanity.com/paper/2503.16395/) (2025)

## Built on by (most cited first, 3 of 3)

- [Incentive Aware AI Regulations: A Credal Characterisation](https://mlsanity.com/paper/2603.05175/) (2026)
- [Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantification](https://mlsanity.com/paper/2605.12208/) (2026)
- [Smoothed Elicitation Complexity for Approximate Gamma-calibration of Discrete Classification Tasks](https://mlsanity.com/paper/2605.23017/) (2026)

## Abstract (arXiv)

Property elicitation studies which attributes of a probability distribution can be determined by minimizing a risk. We investigate a generalization of property elicitation to imprecise probabilities (IP). This investigation is motivated by distributionally robust optimization and multi-distribution learning. Both those frameworks replace the minimization of a single risk over a (precise) probability by a maximin risk minimization over a set of probabilities -- i.e. an IP. We show what can be learned in those multi-distribution setups by providing necessary and sufficient conditions for the elicitability of an IP-property. Central to these conditions is the observation made in related literature that the elicited IP-property is the corresponding classical property of the probability in the IP with the maximum Bayes risk.