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 notions from moral philosophy related to individual and collective, ex-ante and ex-post responsibility in dynamic situations with many agents, complex interaction structures, and different forms of uncertainty.



Major real-world problems, e.g., climate change, involve many heterogeneous agents, conflicting interests, complex dynamic interactions, and different forms of uncertainty. Perceived failures of collective action are often explained by the inefficiency of strategic equilibria arising from agents’ supposed selfishness and individual rationality. Hence the dominant method for studying these problems is game theory and economics, often leading to rather pessimistic predictions. Empirical evidence shows, however, that people are also guided by moral principles, in particular by the concept of responsibility, featuring prominently in public debates, e.g., on climate change. While game-theoretic analyses treat references to responsibility at best as a form of signalling, influencing equilibrium selection, the moral philosophy literature takes the concept much more seriously. While many moral philosophers study different forms of responsibility in simplified fictitious situations, e.g., the famous ‘trolley problem’, more recent work focuses on responsibility in the complex context of climate change.

There are different relevant forms of responsibility:

  • individual vs. collective responsibility
  • ‘ex-ante’ responsibility to act vs. ‘factual ex-post’ responsibility for realized outcomes vs. ‘counterfactual ex-post’
    responsibility for potential outcomes that did not materialize (‘moral luck’)
  • responsibility assigned by an ‘ethical observer’ vs. perceived by the agents themselves
  • qualitative levels vs. quantitative degrees of responsibility
  • etc.

Yet, most of these variants are not sufficiently formalized to be clearly distinguishable, generally applicable, or even measurable. Naïve ad-hoc metrics, e.g., using past cumulative greenhouse-gas emissions to measure ‘historical responsibility’ for climate change, are not readily generalizable. They also fail basic consistency requirements, e.g., regarding the difference between causes and effects. The formal sciences have so far spent little effort on this topic, although some interesting approaches do exist.


Project goals and methods

The project’s goals are to

  • help clarifying, distinguishing, and measuring the various forms of responsibility described above, leading to a mathematical theory of responsibility, by formalizing and testing
    concepts from the philosophical literature with paradigmatic example situations, within a framework compatible with relevant related theories; and to
  • apply the derived theory 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, a very sketch of a “theory of responsibility”, and approaches to enhance game-theoretic models with relevant features ignored by classical models.



After an extensive literature review, we identified a number of paradigmatic example situations and thought experiments used in the moral philosophical literature on responsibility, such as the trolley problem. We translated them into a data structure adapted from extensive-form games. We also identified aspects of responsibility described in the literature, such as individual vs. collective, ex-ante (forward-looking) vs. ex-post (backward-looking), factual vs. counter-factual, assigned vs. perceived responsibility, etc. We then related these aspects of responsibility to features of the formal representation of the example situations. From this, we derived candidate assessments of the various forms of individual and collective responsibility in these situations. We used these assessments as ‘boundary conditions’ for prospective general qualitative and quantitative measures of the various forms of responsibility. In addition, we formulated a set of axioms representing desirable properties of such measures.

Example of ex post responsibility assessment

Assessment of the degree of ex-post 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 ex-post” 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 (a case of moral luck for the robber) and even though the doctor actually chose the regular treatment (which the robber was not allowed to count on however). 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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