We give examples of computing the path-specific harm in Appendices B-D. Omission Problem: Alice decides not to give Bob a set of golf clubs. Therefore, according to the CCA, Alice's decision not to give Bob the'Bob given clubs', and outcome Whatever utility function describes Bob's preferences, the action Note there are other reasonable scenarios where Alice's actions would constitute harm. 'the clerk Alice harmed Bob by not giving him golf clubs'. For example, if Bob's utility is U ( y)= y (i.e. 1 for clubs, 0 for no clubs), then the harm caused by Alice is P ( Y A moment later, Eve would have robbed Bob of his clubs.

We give examples of computing the path-specific harm in Appendices B-D. Omission Problem: Alice decides not to give Bob a set of golf clubs. Therefore, according to the CCA, Alice's decision not to give Bob the'Bob given clubs', and outcome Whatever utility function describes Bob's preferences, the action Note there are other reasonable scenarios where Alice's actions would constitute harm. 'the clerk Alice harmed Bob by not giving him golf clubs'. For example, if Bob's utility is U ( y)= y (i.e. 1 for clubs, 0 for no clubs), then the harm caused by Alice is P ( Y A moment later, Eve would have robbed Bob of his clubs.

As autonomous systems rapidly become ubiquitous, there is a growing need for a legal and regulatory framework to address when and how such a system harms someone. There have been several attempts within the philosophy literature to define harm, but none of them has proven capable of dealing with with the many examples that have been presented, leading some to suggest that the notion of harm should be abandoned and "replaced by more well-behaved notions". As harm is generally something that is caused, most of these definitions have involved causality at some level. Yet surprisingly, none of them makes use of causal models and the definitions of actual causality that they can express. In this paper we formally define a qualitative notion of harm that uses causal models and is based on a well-known definition of actual causality (Halpern, 2016). The key novelty of our definition is that it is based on contrastive causation and uses a default utility to which the utility of actual outcomes is compared. We show that our definition is able to handle the examples from the literature, and illustrate its importance for reasoning about situations involving autonomous systems.

To act safely and ethically in the real world, agents must be able to reason about harm and avoid harmful actions. However, to date there is no statistical method for measuring harm and factoring it into algorithmic decisions. In this paper we propose the first formal definition of harm and benefit using causal models. We show that any factual definition of harm must violate basic intuitions in certain scenarios, and show that standard machine learning algorithms that cannot perform counterfactual reasoning are guaranteed to pursue harmful policies following distributional shifts. We use our definition of harm to devise a framework for harm-averse decision making using counterfactual objective functions. We demonstrate this framework on the problem of identifying optimal drug doses using a dose-response model learned from randomized control trial data. We find that the standard method of selecting doses using treatment effects results in unnecessarily harmful doses, while our counterfactual approach allows us to identify doses that are significantly less harmful without sacrificing efficacy.

In a companion paper (Beckers et al. 2022), 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 lest harmful of a set of possible interventions. 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.