# Quantifying Harm

arXiv: https://arxiv.org/abs/2209.15111 · HTML: https://mlsanity.com/paper/2209.15111/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 48 references that are in the map.
- First posted on arXiv 29 Sep 2022.

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

- [A Modification of the Halpern-Pearl Definition of Causality](https://mlsanity.com/paper/1505.00162/) (2015)
- [Personalized Decision Making -- A Conceptual Introduction](https://mlsanity.com/paper/2208.09558/) (2022)
- [Causal Sufficiency and Actual Causation](https://mlsanity.com/paper/2102.02311/) (2021)
- [Counterfactual harm](https://mlsanity.com/paper/2204.12993/) (2022)
- [On Modeling Human Perceptions of Allocation Policies with Uncertain Outcomes](https://mlsanity.com/paper/2103.05827/) (2021)

## Built on by (most cited first, 10 of 10)

- [A Causal Analysis of Harm](https://mlsanity.com/paper/2210.05327/) (2022)
- [Can a Bayesian Oracle Prevent Harm from an Agent?](https://mlsanity.com/paper/2408.05284/) (2024)
- [Controlling Counterfactual Harm in Decision Support Systems Based on Prediction Sets](https://mlsanity.com/paper/2406.06671/) (2024)
- [A Measure-Theoretic Axiomatisation of Causality](https://mlsanity.com/paper/2305.17139/) (2023)
- [Hybrid Approaches for Moral Value Alignment in AI Agents: a Manifesto](https://mlsanity.com/paper/2312.01818/) (2023)
- [Do No Harm: A Counterfactual Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/2405.11669/) (2024)
- [Nondeterministic Causal Models](https://mlsanity.com/paper/2405.14001/) (2024)
- [Matchings, Predictions and Counterfactual Harm in Refugee Resettlement Processes](https://mlsanity.com/paper/2407.13052/) (2024)
- [Towards Developing Ethical Reasoners: Integrating Probabilistic Reasoning and Decision-Making for Complex AI Systems](https://mlsanity.com/paper/2502.21250/) (2025)
- [Path-specific harm decomposition: A partial identification framework](https://mlsanity.com/paper/2609.29938/) (2026)

## Abstract (arXiv)

In earlier work we defined a qualitative notion of harm: either harm is caused, or it is not. For practical applications, we often need to quantify harm; for example, we may want to choose the least harmful of a set of possible interventions. In this work, which is an expanded version of an earlier conference paper, we develop a quantitative notion of harm. We first present a quantitative definition of harm in a deterministic context involving a single individual, then we consider the issues involved in dealing with uncertainty regarding the context and going from a notion of harm for a single individual to a notion of "societal harm", which involves aggregating the harm to individuals. We show that the "obvious" way of doing this (just taking the expected harm for an individual and then summing the expected harm over all individuals) can lead to counterintuitive or inappropriate answers, and discuss alternatives, drawing on work from the decision-theory literature. Finally, we connect our work to a recent debate over harm within the context of precision medicine.