We present a novel survey module to quantitatively elicit individual uncertainty attitudes through an interactive staircase procedure, which is in analogy to the established procedure for eliciting risk attitudes. We apply it in an experimental field study in the coastal region of Krummhörn, Germany, which is facing climate change and adaptation challenges typical for many low-lying rural coastal areas worldwide. We combine the novel uncertainty preference survey module with experiments to measure risk and time preferences along with socio-demographic variables. We find strong and consistent patterns of the effects of risk preferences, education, age, and happiness on uncertainty preferences of participants in the study region. Furthermore, we confirm that subjects predominantly show decreasing relative uncertainty preferences.

How to ascertain causal relationships has been a key question in science and philosophy for centuries. Based on established principles of causation, we develop a quantitative measure of an agent’s causal responsibility for the state of a dynamical system: we measure the degree to which an agent’s action has caused the system state at a later point in time as the degree to which the action is necessary and sufficient for this state. Our concept can be applied in deterministic as well as in stochastic systems, and for continuous and discrete conceptions of the system state. We find that the extent of causal responsibility crucially depends on the specifics of system dynamics, type of action and the point in time at which the system state occurs. Quantitatively measuring causation in dynamical systems is relevant for attributing an observed system state to its causes, assessing the effectiveness of management actions and policies, or designing liability regulations. Our concept also provides information about the temporal extent of an agent’s causal efficacy and, hence, the temporal limits of the agent’s normative responsibility.

Many fisheries worldwide are not operating sustainably. Returning to sustainable levels is challenging as fisheries are embedded in complex marine social-ecological systems, and bringing the system back to a path of sustainability will likely involve conflicts and tough choices. A first step towards such a path relates to understanding the (different) normative notions of sustainability held by different stakeholder groups. We use the (German) Western Baltic Sea as a case study to elicit these views. At a workshop with representatives of relevant stakeholder groups, we conducted a questionnaire-based survey. Questions were inspired by the stochastic-viability-conceptualisation of strong ecological-economic sustainability under uncertainty. The survey focused on sustainability as a normative goal for fisheries management from a societal perspective. It returned quantitative results which can be directly utilized in fisheries management. We found considerable variation across as well as within stakeholder groups in their normative views on sustainability. Still, it seemed to be consensus among all stakeholders that the different groups have legitimate claims in the Western Baltic Sea, providing common ground on how to sustainably use the WBS. A well-designed transdisciplinary approach with broad exchange between different stakeholders and science seems useful to steer the WBS into a sustainable future.

Many fisheries worldwide are not operating sustainably. Returning to sustainable levels is challenging as fisheries are embedded in complex marine social-ecological systems and bringing the system back to a path of sustainability will likely involve conflicts and tough choices. A first step towards a path of sustainability relates to understanding the (different) normative notions of sustainability held by different stakeholder groups. We use the (German) Western Baltic Sea as a case study to elicit these normative views. At a workshop with representatives of relevant stakeholder groups, we conducted a questionnaire-based survey. Questions were inspired by the stochastic-viability-conceptualization of strong ecological-economic sustainability under uncertainty. The survey focused on sustainability as a normative goal for fisheries management from a societal perspective. It returns quantitative results which can be directly utilized in fisheries management. We find considerable variation across as well as within stakeholder groups in their normative views on sustainability. Still, it seems to be consensus among all stakeholders that the different groups have legitimate claims to the Western Baltic Sea, providing common ground on how to sustainably use the WBS, and a well-designed transdisciplinary approach with broad exchange between different stakeholders and science seems useful to steer the WBS into a sustainable future.

We develop one-parameter preference functions for payoff situations in which the decision maker knows the potential states of nature and their payoffs, but not the probability of these states (Knightian uncertainty). Focusing on the extreme version of Knightian uncertainty, we do not employ probabilities, beliefs or anything alike. Instead, the functions build on the idea that a more (un)even distribution of payoff over states of nature is more (un)certain. We define desirable properties of a preference function (symmetry, non-satiation, uncertainty aversion, invariance under various state-space modifications, decomposability) and show which preference function fulfills which property. In particular, the Atkinson-based preference function captures many desirable properties. The preference functions can be used to study questions of efficient allocation under Knightian uncertainty, including in long-term environmental settings with deep uncertainty, such as investment in climate change adaption.

We construct a generic ecosystem model that features the basic mechanisms of alternative stable states as well as two different stochastic influences. In particular, we use a mean‐reverting jump‐diffusion process to model the evolution of the ecosystem state over time. We review key concepts of multistability theory and the simple heuristics commonly employed to illustrate them. We then provide mathematical definitions for these concepts in the model context. Our contribution to the literature is twofold: we improve the representation of stochasticity in, and clarify key concepts of, multistability theory. The simplicity of the model enables a number of applications, such as finding economically optimal management strategies, identifying criteria for sustainable ecosystem management in a stochastic viability framework, deriving the probability of a regime shift, or empirically identifying the factors which have caused a specific regime shift.

We develop an attribution of collective causal responsibility to individual actors in stochastic nonlinear systems: we take an existing measure of collective causal responsibility from Vallentyne (2008) and Baumgärtner (2020), introduce four elementary axioms on the attribution of collective responsibility to individuals, and propose a measure of individual causal responsibility that is uniquely implied by these axioms. Our approach is inspired by Shapley's (1953) fundamental concept of how to divide a collective effect into individual marginal contributions. The generic setting is a set of systems with potential regime shifts where actions affect the regime-shift probabilities -- e.g. technical systems, traffic systems, financial markets, managed ecosystems, or the Earth's climate system. This paper closes several gaps in the literature on responsibility attribution: our concept is intensive, has cardinal properties and allows for multiple actors with simultaneous actions. This is relevant for implementing efficient incentive schemes and liability for managers of stochastic systems.

Climate change impacts and adaptation measures are subject to various uncertainties. In communication and decision-making, these uncertainties need to be adequately considered. However, uncertainty is a conceptually multifaceted issue, a plethora of connotations and meanings surround the term, and most of that is not explicit but only implicit. We examined the notions of climate-change-related uncertainties actually held by stakeholders – from government and administration, water management, agriculture, tourism, nature conservation, education, and the insurance industry – in the coastal region of Krummhörn, East Frisia, Germany. We employed qualitative, semi-structured in-depth interviews, covering general as well as context-specific aspects of uncertainty. To analyze the interviews, we employed qualitative content analysis, using MAXQDA software and deductively and inductively formed codes. One main finding was the large heterogeneity in the responses: different stakeholders hold widely differing notions of uncertainty – across and even within sectors. Most stakeholders do not normally employ one of the established scientific concepts of uncertainty, but hold a normative perspective on uncertainty which is strongly based on subjective valuation. When dealing with objective information on the quantification of uncertainty, such as probabilities, most stakeholders are inconsistent. The particular perspective on uncertainty is strongly related to the specific topic. On a meta-level, we found that all stakeholders were unfamiliar with talking about uncertainty and had difficulties expressing their ideas in language. Overall, our study confirmed that uncertainty is a contested, pluralistic, and complex phenomenon, which is looked at from different perspectives by different stakeholders. We conclude that the communication of uncertainty at the science–society interface requires particular attention, as the notions of uncertainty held by stakeholders are not always in line with the established scientific concepts of uncertainty.

We study how income inequality affects the social value of a dynamic public good, such as natural capital. Our theory shows that both intra- and intertemporal inequality affect the social value of public natural capital. The direction and size of the effects are driven by the degree of substitutability between the public and private consumption goods. While the value of the public good increases (decreases) with intratemporal income inequality in the case of complements (substitutes), it increases (may decrease) with intertemporal income inequality for complements and Cobb-Douglas (substitutes). A problem of major relevance for the accounting of public natural capital as required by international treaties is to transfer values between study and policy contexts, or to up-scale values from study sites to the national scale. Our theory provides closed-form adjustment factors that allow controlling for differences in study and policy contexts.

I develop a quantitative measure of a manager's responsibility for a regime shift in a managed ecosystem with stochastic dynamics. I build on the well-established concept of responsibility, which I operationalize in a simple generic model. Causal responsibility is the degree of causation of an outcome due to the manager's action, which is in contrast to chance influences that may also have caused the outcome ("good luck'' or "bad luck''). Normative responsibility is the manager's obligation to see to it that the system is in, or shifts to, a specified desired state. It implies a particular management action. Virtuous responsibility is the degree to which the manager lives up to her normative responsibility when taking a management action. The quantitative measurement of responsibility is relevant to judge management actions, to reward or punish the manager based on the extent of her (ir)responsibility, and to design institutions that enable and encourage responsible management of ecosystems with potential regime shifts.

I derive an approximation for the welfare change between two risky income prospects. For two special cases, constant absolute risk-aversion and constant relative risk-aversion, one can give an exact expression for the welfare change. At core, the exact and the approximate expressions for the welfare change build on the change in the certainty equivalent between the two risky income prospects. These results are useful for both theoretical and empirical work on risk valuation, as they provide simple and easy-to-use proxies.

We characterize intertemporal utility functions over heterogeneous goods that feature (i) a constant elasticity of substitution between goods at each point in time and (ii) a constant intertemporal elasticity of substitution for at least one of the goods. We find that a standard, stationary intertemporal utility function is consistent with these two properties if and only if it either is of the intertemporal constant elasticity of substitution (ICES) form, that is, if all elasticities of substitution are identical, or if the instantaneous utility function is Cobb–Douglas. We also characterize the families of stationary intertemporal utility functions that feature either (i) or (ii), but not the respective other property.

We survey the emerging research area of sustainability economics through a quantitative full-text analysis of peer-reviewed journal publications from 1987 to 2013. To identify relevant contributions, we draw on existing definitions of sustainability economics for a keyword-based identification strategy: a combined focus on (a) the human-nature relationship, (b) the long-term uncertain future, (c) normative orientation towards sustainability, and (d) economic analysis. Our analysis of a random subsample of 343 relevant papers reveals that (i) sustainability economics is a rapidly developing research area; (ii) while theoretical contributions shaped the area in earlier years, applied work now constitutes the largest share of contributions; (iii) the research landscape can be clustered into eleven research clusters. These range from participatory governance of social-ecological systems associated with the work of Elinor Ostrom to questions of intertemporal allocation and distribution applied to climate economics associated with the work of William Nordhaus; (iv) the research area is broad in scope and heterogeneous, and there is relatively little interaction between important clusters; (v) relevant contributions are published in more than 100 journals. Ten journals publish half of all contributions, led by Ecological Economics, and 40% appear in non-economics journals, underscoring the importance of interdisciplinary dialogue.

Nature-based solutions to insurance are in high demand. We explore the idea that natural capital has an insurance value insofar as it can mitigate the effects of uncertainty on human well-being. We present a formal model that substantiates this claim. We propose a definition for the insurance value of natural capital for a stochastic and dynamic ecosystem that provides ecosystem services for a risk-averse user. The insurance value of natural capital depends on the properties of ecosystem dynamics as well as on the risk and time preferences of the ecosystem user. It can be positive or negative. We relate the natural insurance value to conservative use of the ecosystem and precautionary investment in the natural capital stock. For the case of logarithmic per-period utility we find that optimal management becomes more conservative with increasing uncertainty if and only if the insurance value of natural capital is positive. We qualify this finding for more general forms of the per-period utility function.

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Utilizing a data set of 399 Namibian commercial cattle farmers, we provide a detailed empirical analysis of farm management under highly variable rainfall. Particularly, we provide an econometric analysis of what personal characteristics of the farmer, environmental characteristics, and characteristics of the farm explain farm size and choice of stocking rate, i.e. the heads of livestock per hectare. There is strong support for the hypothesis that environmental variables such as inter-annual rainfall variability play an important role in explaining stocking rate, but not in explaining farm size in the sense of rangeland area or cattle numbers. Other major explaining factors for the stocking rate are the farmer's gender and the number of cattle on farm above a certain threshold given by a fit of the Pareto distribution to the data. Traditional farm size variables like cattle number and rangeland area are not well explained by any of the candidate models constructed, which supports the view that the stocking rate is the central farm management parameter.

This paper studies how the intraand intergenerational distribution of income and wealth affect the economic valuation of environmental public goods derived from natural capital. We consider both a single payment or a constant payment fraction share over time and the willingness to pay (WTP) for a marginal change of the level or the growth rate of the environmental public good. We find that the intragenerational distribution affects the intertemporal valuation of environmental goods derived from natural capital. We show that for both payment vehicles, societal mean WTP for the level as well as the growth rate of natural capital decreases (increases) with intratemporal income inequality if environmental goods derived from natural capital and consumption goods are substitutes (complements). We obtain closed-form adjustment factors for benefit transfer to control for differences in dynamic aspects between study and policy sites, such as income growth, the growth rate of the environmental goods, and interest rates. Our results are relevant for the economic appraisal of environmental policy as well as natural capital accounting and management. JEL-Classification: D63, H43, Q51