# Statistical Decision Theory with Counterfactual Loss

arXiv: https://arxiv.org/abs/2505.08908 · HTML: https://mlsanity.com/paper/2505.08908/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 44 references that are in the map.
- First posted on arXiv 13 May 2025.

## Builds on (most cited first, 12 of 12)

- [Counterfactual Risk Assessments, Evaluation, and Fairness](https://mlsanity.com/paper/1909.00066/) (2019)
- [Personalized Decision Making -- A Conceptual Introduction](https://mlsanity.com/paper/2208.09558/) (2022)
- [Counterfactual harm](https://mlsanity.com/paper/2204.12993/) (2022)
- [Probabilities of Causation with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09568/) (2022)
- [Principal Fairness for Human and Algorithmic Decision-Making](https://mlsanity.com/paper/2005.10400/) (2020)
- [Experimental Evaluation of Algorithm-Assisted Human Decision-Making: Application to Pretrial Public Safety Assessment](https://mlsanity.com/paper/2012.02845/) (2020)
- [What's the Harm? Sharp Bounds on the Fraction Negatively Affected by Treatment](https://mlsanity.com/paper/2205.10327/) (2022)
- [Unit Selection with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09569/) (2022)
- [Policy Learning with Asymmetric Counterfactual Utilities](https://mlsanity.com/paper/2206.10479/) (2022)
- [Does AI help humans make better decisions? A statistical evaluation framework for experimental and observational studies](https://mlsanity.com/paper/2403.12108/) (2024)
- [Unit Selection: Case Study and Comparison with A/B Test Heuristic](https://mlsanity.com/paper/2210.05030/) (2022)
- [A general theory of identification](https://mlsanity.com/paper/2002.06041/) (2020)

## Built on by (most cited first, 2 of 2)

- [Synthetic Counterfactual Labels for Efficient Conformal Counterfactual Inference](https://mlsanity.com/paper/2509.04112/) (2025)
- [Confronting Label Indeterminacy in Automated Bail Decisions](https://mlsanity.com/paper/2605.04073/) (2026)

## Abstract (arXiv)

Many researchers apply classical statistical decision theory to evaluate treatment choices and learn optimal policies. However, because this framework relies solely on realized outcomes under chosen actions and ignores counterfactuals, it cannot assess the quality of a decision relative to feasible alternatives at the unit level, which is an important requirement in some settings. For example, in pretrial bail decisions, a judge must balance crime prevention upon release against the risk of imposing unnecessary burdens on arrestees. A central challenge in this framework is identification: since only one potential outcome is observed per unit, counterfactual risk is typically not identifiable. We show that, under strong ignorability, counterfactual risk is identifiable if and only if the loss is additive in the potential outcomes. We further demonstrate that additive counterfactual losses can yield treatment recommendations that differ from those based on standard losses when more than two treatment options are available. We show that additive counterfactual losses capture not only decision accuracy but also decision difficulty, whereas standard losses reflect accuracy alone. Finally, we introduce a symbolic linear inverse program that determines whether a given counterfactual loss yields an identifiable risk, without requiring data.