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

01.01.2019 – 31.12.2021

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.

Guiding hypotheses of this project are that notions of responsibility

  • play an important role in human collective decision making and
  • call for a clean and flexible mathematical formalization to facilitate
    their incorporation into related established modeling frameworks, such
    as game, control, and Bayesian decision theory.

As a baseline, such a formalization should account for ethical evaluations of the uncertain consequences of possible and actual actions of agents. In order to avoid a so-called “diffusion of responsibility”, a proper theory must distinguish probabilistic uncertainty with known probabilities from uncertainty due to others agents’ unknown decisions by free will, and from other forms of uncertainty, e.g. when only probability intervals are given, as in the reports by the IPCC.

In approaching this challenge, the project builds on preliminary work on the formalization of ‘vulnerability’ and ‘resilience’ in the context of climate change, and proposes to enhance the aforementioned game-theoretic responsibility models with a broader view of causation applicable here.



After an extensive literature review, we first 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 as well as paradigmatic example situations and thought experiments used in the moral philosophical literature on responsibility. Concerning for example the conditions needed for backwards-looking moral responsibility ascription, variations of the following are consistently named in the literature:

  • 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.
    ⇒ In contrast to the existing literature we adopt a probability raising account of causation. That is, an action is causally related to an undesired outcome to the degree that this action increased its likelihood.
  • Avoidance condition. The agent must have had a reasonable chance to act differently.

    ⇒ We consider all actions presented in the model as reasonable. This condition is included as one of the axioms we want our responsibility functions to fulfill.

We translated relevant decision scenarios for which we want to compute responsibility scores into a data structure adapted from extensive-form games. Within these situations, we derived candidate assessments of the various forms of individual and collective backwards- and forwards-looking responsibility. We used the assessments of the paradigmatic example scenarios as ‘boundary conditions’ for proposed responsibility functions, and defined other desirable properties as ‘axioms’ for their characterization.

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.

We then designed several first candidate versions of measures of responsibility aiming to fulfill as many of these boundary conditions and axioms, and applied them to a number of exemplary situations, mainly from social choice theory. A first publication on this in currently in revision [1].

Project Webpages

Selected Publications

1. Heitzig J, Hiller S (2020) Degrees of individual and groupwise backward and forward responsibility in extensive-form games with ambiguity, and their application to social choice problems. In revision.

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