Vulnerability: From the conceptual to the operational using a dynamical system perspective. (November 2015) - Rougé, Charles; Mathias, Jean-Denis; Deffuant, Guillaume
Abstract: This work proposes to address a lack of conceptual consensus surrounding the concept of vulnerability, by fostering a minimal definition as a measure of potential future harm, and by basing it on a stochastic controlled dynamical system framework. Harm is defined as a normative judgment on a trajectory. Considering all the possible trajectories from an initial state leads to the definition of vulnerability indicators as statistics derived from the probability distribution of harm values. This framework 1) promotes a dynamic view of vulnerability by eliciting its temporal dimension and 2) clarifies the descriptive and normative aspects of a system's representation. As illustrated by a simple model of lake eutrophication, this work makes vulnerability a precise yet flexible concept which fosters discussion on trade-offs between vulnerability sources, and also on adaptation. Links with economics, with control theory, and with algorithmic methods such as dynamic programming are highlighted. Highlights: Vulnerability is an increasingly oft-used concept, yet remains ill-defined. A formal mathematical framework is proposed to lift ambiguity. Framework integrates system dynamics, stakeholders' decisions, and uncertainties. Framework helps design varied indicators; fosters exploration of relevant policies. Framework is a useful reference even when a system's equations are unknown.