EF5 – Concepts of Change in Historical Processes



A Mathematical Theory of Responsibility in Complex Multi-Agent Decision Problems with Uncertainties

Project Heads

Rupert Klein, Jobst Heitzig, Markus Brill

Project Members

Sarah Hiller (FU) 

Project Duration

15.09.2019 – 14.09.2022

Located at

FU Berlin


Motivated by the needs of climate change research, this project aims to formalize the concept of moral responsibility, both backward- and forward-looking, in interactive multi-agent decision scenarios with various levels of uncertainty.




The current climate crisis and its associated effects constitute one of the essential challenges for humanity and collective decision making in the upcoming years. Naturally, the public debate around this issue frequently invokes the question of responsibility: Who carries how much backward-looking responsibility for the changes already inevitable, who is to blame; and who carries how much forward-looking responsibility to realize changes, who has to act?

In the current project we aim for a formal representation of the concept of moral responsibility in particular, in order to make precise what is being talked about and to allow for a quantified measure for responsibility ascription. As collective action in face of the climate crisis is the initial motivation for this research question, it will also be the application scenario that we ultimately test our achievements on. However, several features inherent to this scenario complicate responsibility assignments:

  • Anthropogenic climate change as well as its possible mitigation is innately the result of a collective and interactive action.
  • There is considerable uncertainty in several areas such as the precise results of specific actions or the actions of other agents.

  • The decision making is not a one-off event but rather embedded into a temporal progression.

Previous work regarding formalizations of moral responsibility in the context of climate change can roughly be divided into two categories, via the perspective from which this question is addressed. On the one side there are considerations focusing on applicability in the climate change context, using naïve ad-hoc measures for this specific area with the advantage of being easy to compute but disregarding generalisability. On the other side there is considerable work in formal ethics, aiming at understanding and formally representing the concept of responsibility in general with a special focus on rigor and well-foundedness, making it harder to account for messy real world scenarios.


Project goals and methods

The project’s goals are to

  • contribute to a mathematical theory of responsibility by developing a framework for the representation of relevant decision scenarios
  • define representations of responsibility ascription within this framework
  • identify from the literature as well as from additional considerations paradigmatic example scenarios and other desirable properties in order to evaluate proposed responsibility functions
  • evaluate and ideally characterise the set of responsibility functions according to these features
  • apply the derived measure to real-world problems such as climate change.

As a baseline, such a formalization should account for ethical evaluations of the uncertain consequences of possible and actual actions of agents.

We employ a variety of methods from different fields throughout the analysis. First, the representation of decision situations in which we want to assign responsibility is achieved through an extension of extensive-form games, giving us the necessary tools to talk about responsibility in a formal way. Proposed responsibility functions are then evaluated according to their performance in selected paradigmatic example scenarios or via an axiomatic method. Finally, the selected functions will be applied in a real-world scenario, which will be computed using climate modelling. 



As a first step, we identified taxonomies of the various meanings of the term ‘responsibility’. The kind that we are interested in concerns the moral evaluation of actions of intentionally acting agents. It is more restrictive than a simple causal connection but does not go as far as legal liability. Also, unlike an impartial causal responsibility the kind that we focus on presupposes a relation to an ethically undesired outcome. We therefore name it ‘moral responsibility’.

Subsequently, we extracted criteria for responsibility ascription used in the moral philosophical literature on responsibility. Variations of the following are consistently named:

  • Capacity condition. The agent is able to act intentionally and has basic moral reasoning. For example, dogs or small children are exempt from moral responsibility judgements.
    ⇒ In line with the literature, we assume that agents for whom this does not hold are left out of the model.
  • Causality condition. The agent is in some relevant sense causally related to the outcome in question.
    ⇒ The biggest novelty of our work is contained in this condition. Instead of causation we consider probability raising as a ground for responsibility ascription. Currently, we evaluate whether a probabilistic notion of causation can also be employed.
  • Avoidance condition. The agent must have had a reasonable chance to act differently. ⇒ This condition is included as one of the axioms we want our responsibility functions to fulfill. We consider all actions presented in the model as reasonable. 

We translated relevant decision scenarios for which we want to compute responsibility scores into a data structure adapted from extensive-form games. 

Example of ex post responsibility assessment

Assessment of the degree of backwards-looking responsibility in an example situation discussed in the moral philosophy literature. A robber (1) has stabbed a victim, knowing that a doctor (2) would administer either a negligent or a regular treatment, leading to different probabilities of survival (★). In one variant of the responsibility measure, the robber is assigned 50% “counterfactual” responsibility for the victim’s possible death, which is the difference between the worst-case probability of death in the two branches of the extensive-form tree that the robber could choose from. This is even though the victim lived as the doctor actually chose the regular treatment. This constitutes a case of moral luck for the robber, which, however, we argue they were not allowed to count on. Other variants come to different assessments since they treat the unquantifiable uncertainty of what the doctor would do in a different way.

Within these situations, we derived candidate assessments of the various forms of individual and collective backwards- and forwards-looking responsibility. In a first step we then used assessments of paradigmatic example scenarios as ‘boundary conditions’ for the proposed responsibility functions.

In a next step the comparison of proposed functions was carried out more formally using an axiomatic method. That is, we determined desirable properties of the functions as ‘axioms’ and evaluated implications, incompatibilities and characterizations of these axioms.

Project Webpages

Selected Publications

1. Hiller S, Heitzig J (2021) Quantifying Responsibility with Probabilistic Causation — The Case of Climate Action. arXiv preprint https://arxiv.org/abs/2111.02304

2. Hiller S, Israel J, Heitzig J (2021) An Axiomatic Approach to Formalized Responsibility Ascription. arXiv preprint https://arxiv.org/abs/2111.06711

Selected Pictures

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