arXiv subjects

Jobst Heitzig

Publications and source records attributed to Jobst Heitzig.

At least 37 records · Page 2Linked to original sources

arXiv2023

Improving International Climate Policy via Mutually Conditional Binding Commitments

This paper proposes enhancements to the RICE-N simulation and multi-agent reinforcement learning framework to improve the realism of international climate policy negotiations. Acknowledging the framework's value, we highlight the necessity of significant enhancements to address the diverse array of factors in modeling climate negotiations. Building upon our previous work on the "Conditional Commitments Mechanism" (CCF mechanism) we discuss ways to bridge the gap between simulation and reality. We suggest the inclusion of a recommender or planner agent to enhance coordination, address the Real2Sim gap by incorporating social factors and non-party stakeholder sub-agents, and propose enhancements to the underlying Reinforcement Learning solution algorithm. These proposed improvements aim to advance the evaluation and formulation of negotiation protocols for more effective international climate policy decision-making in Rice-N. However, further experimentation and testing are required to determine the implications and effectiveness of these suggestions.

cs.CY↗

arXiv2023

Improving International Climate Policy via Mutually Conditional Binding Commitments

The Paris Agreement, considered a significant milestone in climate negotiations, has faced challenges in effectively addressing climate change due to the unconditional nature of most Nationally Determined Contributions (NDCs). This has resulted in a prevalence of free-riding behavior among major polluters and a lack of concrete conditionality in NDCs. To address this issue, we propose the implementation of a decentralized, bottom-up approach called the Conditional Commitment Mechanism. This mechanism, inspired by the National Popular Vote Interstate Compact, offers flexibility and incentives for early adopters, aiming to formalize conditional cooperation in international climate policy. In this paper, we provide an overview of the mechanism, its performance in the AI4ClimateCooperation challenge, and discuss potential real-world implementation aspects. Prior knowledge of the climate mitigation collective action problem, basic economic principles, and game theory concepts are assumed.

cs.CY↗

arXiv2023

Resilience basins of complex systems: an application to prosumer impacts on power grids

Comparable to the traditional notion of stability in system dynamics, resilience is typically measured in a way that assesses the quality of a system's response, for example the speed of its recovery. We present a broadly applicable complementary measurement framework that quantifies resilience similarly to basin stability by estimating a "resilience basin" which reflects the extent of adverse influences that the system can recover from in a sufficient manner. In contrast to basin stability, the adverse influences considered here are not necessarily displacements in state space, but arbitrarily complex impacts to the system, quantified by adequate parameters. As a proof of concept, we present two applications: (i) the well-studied single-node power system as an easy-to-follow example and (ii) a stochastic model of a low-voltage DC power grid undergoing an unregulated energy transition consisting in the random appearance of prosumers. These act as decentral suppliers of photovoltaic power and alter the flow patterns while the grid topology remains unchanged. The resilience measurement framework is applied to evaluate the effect and efficiency of two response options: (i) upgrading the capacity of existing power lines and (ii) installing batteries in the prosumer households. The framework demonstrates that line upgrades can provide potentially unlimited resilience against energy decentralization, while household batteries are inherently limited (achieving <=70% of the resilience of line upgrades). Further, the framework aids in optimizing budget efficiency by pointing toward threshold budget values as well as budget-dependent ideal strategies for the allocation of line upgrades and for the battery charging algorithm.

physics.soc-ph↗

arXiv2023

Probability-Based Estimation

We develop a theory of estimation when in addition to a sample of $n$ observed outcomes the underlying probabilities of the observed outcomes are known, as is typically the case in the context of numerical simulation modeling, e.g. in epidemiology. For this enriched information framework, we design unbiased and consistent ``probability-based'' estimators whose variance vanish exponentially fast as $n\to\infty$, as compared to the power-law decline of classical estimators' variance.

stat.ME↗

arXiv2022

An Axiomatic Approach to Formalized Responsibility Ascription

A formalized and quantifiable responsibility score is a crucial component in many aspects of the development and application of multi-agent systems and autonomous agents. We can employ it to inform decision making processes based on ethical considerations, as a measure to ensure redundancy that helps us in avoiding system failure, as well as for verifying that autonomous systems remain trustworthy by testing for unwanted responsibility voids in advance. We follow recent proposals to use probabilities as the basis for responsibility ascription in uncertain environments rather than the deterministic causal views employed in much of the previous formal philosophical literature. Using an axiomatic approach we formally evaluate the qualities of (classes of) proposed responsibility functions. To this end, we decompose the computation of the responsibility a group carries for an outcome into the computation of values that we assign to its members for individual decisions leading to that outcome, paired with an appropriate aggregation function. Next, we discuss a number of intuitively desirable properties for each of these contributing functions. We find an incompatibility between axioms determining upper and lower bounds for the values assigned at the member level. Regarding the aggregation from member-level values to group-level responsibility we are able to axiomatically characterize one promising aggregation function. Finally, we present two maximally axiom compliant group-level responsibility measures -- one respecting the lower bound axioms at the member level and one respecting the corresponding upper bound axioms.

cs.GT↗

arXiv2022

Conceptualizing World-Earth System resilience: Exploring transformation pathways towards a safe and just operating space for humanity

We develop a framework within which to conceptualize World-Earth System resilience. Our notion of World-Earth System resilience emphasizes the need to move beyond the basin of attraction notion of resilience as we are not in a basin we can stay in. We are on a trajectory to a new basin and we have to avoid falling into undesirable basins. We thus focus on `pathway resilience', i.e. the relative number of paths that allow us to move from the transitional operating space we occupy now as we leave the Holocene basin to a safe and just operating space in the Anthropocene. We develop a mathematical model to formalize this conceptualization and demonstrate how interactions between earth system resilience (biophysical processes) and world system resilience (social processes) impact pathway resilience. Our findings show that building earth system resilience is probably our only chance to reach a safe and just operating space. We also illustrate the importance of world system dynamics by showing how the notion of fairness coupled with regional inequality affects pathway resilience.

physics.soc-ph↗

arXiv2021

A modeler's guide to studying the resilience of social-technical-environmental systems

The term 'resilience' is increasingly being used in social-technical-environmental systems sciences and particularly also in the Earth system sciences. However, the diversity of resilience concepts and a certain (sometimes intended) openness of proposed definitions can lead to misunderstandings and may impede their application to complex systems modelling. We propose a guideline that aims to ease communication as well as to support systematic development of research questions and models in the context of resilience. It can be applied independently of the modelling framework or underlying theory of choice. At the heart of this guideline is a checklist consisting of four questions to be answered: (i) Resilience of what? (ii) Resilience regarding what? (iii) Resilience against what? (iv) Resilience how? We refer to the answers to these resilience questions as the "system", the "sustainant", the "adverse influence", and the "response options". The term 'sustainant' is a neologism describing the feature of the system (state, structure, function, pathway, ...) that should be maintained (or restored quickly enough) in order to call the system resilient. The use of this proposed guideline in the field of Earth system resilience is demonstrated for the application example of a potential climate tipping element: the Amazon rainforest. The example illustrates the diversity of possible answers to the checklist's questions as well as their benefits in structuring the modelling process. The guideline supports the modeller in communicating precisely what is actually meant by 'resilience' in a specific context. This combination of freedom and precision could help to advance the resilience discourse by building a bridge between those demanding unambiguous definitions and those stressing the benefits of generality and flexibility of the resilience concept.

physics.soc-ph↗

arXiv2021

Quantifying Responsibility with Probabilistic Causation -- The Case of Climate Action

Many real-world situations of ethical and economic relevance, such as collective (in)action with respect to the climate crisis, involve not only diverse agents whose decisions interact in complicated ways, but also various forms of uncertainty, including both quantifiable risk and unquantifiable ambiguity. In such cases, an assessment of moral responsibility for ethically undesired outcomes or of the responsibility to avoid these is challenging and prone to the risk of under- or over determination. In contrast to existing approaches that employ notions of causation based on combinations of necessity and sufficiency or certain logics that focus on a binary classification of `responsible' vs `not responsible', we present a set of quantitative metrics that assess responsibility degrees in units of probability. To this end, we adapt extensive-form game trees as the framework for representing decision scenarios and evaluate the proposed responsibility functions based on the correct representation of a set of analytically assessed paradigmatic example scenarios. We test the best performing metrics on a reduced representation of a real-world decision scenario and are able to compute meaningful responsibility scores.

physics.soc-ph↗

arXiv2021

Dose-response functions and surrogate models for exploring social contagion in the Copenhagen Networks Study

Spreading dynamics and complex contagion processes on networks are important mechanisms underlying the emergence of critical transitions, tipping points and other nonlinear phenomena in complex human and natural systems. Increasing amounts of temporal network data are now becoming available to study such spreading processes of behaviours, opinions, ideas, diseases and innovations to test hypotheses regarding their specific properties. To this end, we here present a methodology based on dose-response functions and hypothesis testing using surrogate data models that randomise most aspects of the empirical data while conserving certain structures relevant to contagion, group or homophily dynamics. We demonstrate this methodology for synthetic temporal network data of spreading processes generated by the adaptive voter model. Furthermore, we apply it to empirical temporal network data from the Copenhagen Networks Study. This data set provides a physically-close-contact network between several hundreds of university students participating in the study over the course of three months. We study the potential spreading dynamics of the health-related behaviour "regularly going to the fitness studio" on this network. Based on a hierarchy of surrogate data models, we find that our method neither provides significant evidence for an influence of a dose-response-type network spreading process in this data set, nor significant evidence for homophily. The empirical dynamics in exercise behaviour are likely better described by individual features such as the disposition towards the behaviour, and the persistence to maintain it, as well as external influences affecting the whole group, and the non-trivial network structure. The proposed methodology is generic and promising also for applications to other temporal network data sets and traits of interest.

physics.soc-ph↗

arXiv2021

Moving the epidemic tipping point through topologically targeted social distancing

The epidemic threshold of a social system is the ratio of infection and recovery rate above which a disease spreading in it becomes an epidemic. In the absence of pharmaceutical interventions (i.e. vaccines), the only way to control a given disease is to move this threshold by non-pharmaceutical interventions like social distancing, past the epidemic threshold corresponding to the disease, thereby tipping the system from epidemic into a non-epidemic regime. Modeling the disease as a spreading process on a social graph, social distancing can be modeled by removing some of the graphs links. It has been conjectured that the largest eigenvalue of the adjacency matrix of the resulting graph corresponds to the systems epidemic threshold. Here we use a Markov chain Monte Carlo (MCMC) method to study those link removals that do well at reducing the largest eigenvalue of the adjacency matrix. The MCMC method generates samples from the relative canonical network ensemble with a defined expectation value of $λ_{max}$. We call this the "well-controlling network ensemble" (WCNE) and compare its structure to randomly thinned networks with the same link density. We observe that networks in the WCNE tend to be more homogeneous in the degree distribution and use this insight to define two ad-hoc removal strategies, which also substantially reduce the largest eigenvalue. A targeted removal of 80\% of links can be as effective as a random removal of 90\%, leaving individuals with twice as many contacts.

physics.soc-ph↗

arXiv2021

Statistical Analysis of Tipping Pathways in Agent-Based Models

Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here, we are concerned with studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to the large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach.

physics.soc-ph↗

arXiv2020

Modelling nonlinear dynamics of interacting tipping elements on complex networks: the PyCascades package

Tipping elements occur in various systems such as in socio-economics, ecology and the climate system. In many cases, the individual tipping elements are not independent from each other, but they interact across scales in time and space. To model systems of interacting tipping elements, we here introduce the PyCascades open source software package for studying interacting tipping elements (doi: 10.5281/zenodo.4153102). PyCascades is an object-oriented and easily extendable package written in the programming language Python. It allows for investigating under which conditions potentially dangerous cascades can emerge between interacting dynamical systems, with a focus on tipping elements. With PyCascades it is possible to use different types of tipping elements such as double-fold and Hopf types and interactions between them. PyCascades can be applied to arbitrary complex network structures and has recently been extended to stochastic dynamical systems. This paper provides an overview of the functionality of PyCascades by introducing the basic concepts and the methodology behind it. In the end, three examples are discussed, showing three different applications of the software package. First, the moisture recycling network of the Amazon rainforest is investigated. Second, a model of interacting Earth system tipping elements is discussed. And third, the PyCascades modelling framework is applied to a global trade network.

physics.soc-ph↗

arXiv2020

Anticipation-induced social tipping -- Can the environment be stabilised by social dynamics?

In the past decades human activities caused global Earth system changes, e.g., climate change or biodiversity loss. Simultaneously, these associated impacts have increased environmental awareness within societies across the globe, thereby leading to dynamical feedbacks between the social and natural Earth system. Contemporary modelling attempts of Earth system dynamics rarely incorporate such co-evolutions and interactions are mostly studied unidirectionally through direct or remembered past impacts. Acknowledging that societies have the additional capability for foresight, this work proposes a conceptual feedback model of socio-ecological co-evolution with the specific construct of anticipation acting as a mediator between the social and natural system. Our model reproduces results from previous sociological threshold models with bi-stability if one assumes a static environment. Once the environment changes in response to societal behaviour the system instead converges towards a globally stable, but not necessarily desired, attractor. Ultimately, we show that anticipation of future ecological states then leads to metastability of the system where desired states can persist for a long time. We thereby demonstrate that foresight and anticipation form an important mechanism which, once its time horizon becomes large enough, fosters social tipping towards behaviour that can stabilise the environment and prevents potential socio-ecological collapse.

physics.soc-ph↗

arXiv2020

From lakes and glades to viability algorithms: Automatic classification of system states according to the Topology of Sustainable Management

The framework Topology of Sustainable Management by Heitzig et al. (2016) distinguishes qualitatively different regions in state space of dynamical models representing manageable systems with default dynamics. In this paper, we connect the framework to viability theory by defining its main components based on viability kernels and capture basins. This enables us to use the Saint-Pierre algorithm to visualize the shape and calculate the volume of the main partition of the Topology of Sustainable Management. We present an extension of the algorithm to compute implicitly defined capture basins. To demonstrate the applicability of our approach, we introduce a low-complexity model coupling environmental and socioeconomic dynamics. With this example, we also address two common estimation problems: an unbounded state space and highly varying time scales. We show that appropriate coordinate transformations can solve these problems. It is thus demonstrated how algorithmic approaches from viability theory can be used to get a better understanding of the state space of manageable dynamical systems.

math.OC↗

arXiv2020

Social tipping processes for sustainability: An analytical framework

Societal transformations are necessary to address critical global challenges, such as mitigation of anthropogenic climate change and reaching UN sustainable development goals. Recently, social tipping processes have received increased attention, as they present a form of social change whereby a small change can shift a sensitive social system into a qualitatively different state due to strongly self-amplifying (mathematically positive) feedback mechanisms. Social tipping processes have been suggested as key drivers of sustainability transitions emerging in the fields of technological and energy systems, political mobilization, financial markets and sociocultural norms and behaviors. Drawing from expert elicitation and comprehensive literature review, we develop a framework to identify and characterize social tipping processes critical to facilitating rapid social transformations. We find that social tipping processes are distinguishable from those of already more widely studied climate and ecological tipping dynamics. In particular, we identify human agency, social-institutional network structures, different spatial and temporal scales and increased complexity as key distinctive features underlying social tipping processes. Building on these characteristics, we propose a formal definition for social tipping processes and filtering criteria for those processes that could be decisive for future trajectories to global sustainability in the Anthropocene. We illustrate this definition with the European political system as an example of potential social tipping processes, highlighting the potential role of the FridaysForFuture movement. Accordingly, this analytical framework for social tipping processes can be utilized to illuminate mechanisms for necessary transformative climate change mitigation policies and actions.

physics.soc-ph↗

arXiv2020

Macroscopic approximation methods for the analysis of adaptive networked agent-based models: The example of a two-sector investment model

In this paper, we propose a statistical aggregation method for agent-based models with heterogeneous agents that interact both locally on a complex adaptive network and globally on a market. The method combines three approaches from statistical physics: (a) moment closure, (b) pair approximation of adaptive network processes, and (c) thermodynamic limit of the resulting stochastic process. As an example of use, we develop a stochastic agent-based model with heterogeneous households that invest in either a fossil-fuel or renewables-based sector while allocating labor on a competitive market. Using the adaptive voter model, the model describes agents as social learners that interact on a dynamic network. We apply the approximation methods to derive a set of ordinary differential equations that approximate the macro-dynamics of the model. A comparison of the reduced analytical model with numerical simulations shows that the approximation fits well for a wide range of parameters. The proposed method makes it possible to use analytical tools to better understand the dynamical properties of models with heterogeneous agents on adaptive networks. We showcase this with a bifurcation analysis that identifies parameter ranges with multi-stabilities. The method can thus help to explain emergent phenomena from network interactions and make them mathematically traceable.

econ.TH↗

arXiv2020

Degrees of individual and groupwise backward and forward responsibility in extensive-form games with ambiguity, and their application to social choice problems

Many real-world situations of ethical relevance, in particular those of large-scale social choice such as mitigating climate change, involve not only many agents whose decisions interact in complicated ways, but also various forms of uncertainty, including quantifiable risk and unquantifiable ambiguity. In such problems, an assessment of individual and groupwise moral responsibility for ethically undesired outcomes or their responsibility to avoid such is challenging and prone to the risk of under- or overdetermination of responsibility. In contrast to existing approaches based on strict causation or certain deontic logics that focus on a binary classification of `responsible' vs `not responsible', we here present several different quantitative responsibility metrics that assess responsibility degrees in units of probability. For this, we use a framework based on an adapted version of extensive-form game trees and an axiomatic approach that specifies a number of potentially desirable properties of such metrics, and then test the developed candidate metrics by their application to a number of paradigmatic social choice situations. We find that while most properties one might desire of such responsibility metrics can be fulfilled by some variant, an optimal metric that clearly outperforms others has yet to be found.

econ.TH↗

arXiv2020

Efficient democratic decisions via nondeterministic proportional consensus

Are there voting methods which (i) give everyone, including minorities, an equal share of effective power even if voters act strategically, (ii) promote consensus rather than polarization and inequality, and (iii) do not favour the status quo or rely too much on chance? We show the answer is yes by describing two nondeterministic voting methods, one based on automatic bargaining over lotteries, the other on conditional commitments to approve compromise options. Our theoretical analysis and agent-based simulation experiments suggest that with these, majorities cannot consistently suppress minorities as with deterministic methods, proponents of the status quo cannot block decisions as in consensus-based approaches, the resulting aggregate welfare is comparable to existing methods, and average randomness is lower than for other nondeterministic methods.

econ.GN↗