Andrea Saltelli

Demographic projections feed directly into some of the highest-stakes risk-management decisions governments make, from pension system solvency to labour-force and fiscal-sustainability planning, yet the uncertainty surrounding these projections is rarely subjected to the kind of structured uncertainty and sensitivity analysis routine in other risk-modelling domains. We examine two case studies that illustrate the resulting risk. The first is a retrospective model-validation exercise on the optimisation-based population model of Song et al., which underpinned China’s one-child policy: applying global uncertainty analysis reveals that the model is, by construction, insensitive to demographic inputs and converges to its predetermined target population of approximately 700 million regardless of parameter variation—a textbook case of a model that obscures rather than informs the risk it claims to manage. The second is a modelling-of-the-modelling-process experiment projecting global population to 2050 and 2075 across seven configurations spanning three projection paradigms (Cohort-Component, Lotka intrinsic growth rate, and ARIMA) and two intra-paradigm sub-model choices, with ten uncertain inputs and 22,528 Sobol’ model evaluations. The choice of projection paradigm alone accounts for 87–90% of output variance, dwarfing all parametric uncertainty combined; intra-paradigm sub-model choices contribute a further 2–5%. We show that current policy-relevant demographic inputs—including the European Commission’s 2024 Ageing Report and an IMF Staff Discussion Note on pension systemdesign—rely on single demographic models with no structural uncertainty quantification, leaving a substantial, unrecognised source of model risk embedded in fiscal and pension policy. We conclude with concrete, transferable heuristics for distinguishing genuine decision-support models from models that function as advocacy instruments wrapped in mathematical form, of direct relevance to risk analysts validating models in any domain where structural model choice, not just parametric uncertainty, drives decision-relevant variance.

University rankings powerfully shape strategy and policy, yet they say little about what students pay. This paper introduces a simple, replicable benchmark that juxtaposes posted undergraduate fees with rank positions for 112 European universities listed in both ARWU and THE WUR (2018). Using a combined rank indicator and descriptive comparisons, we show a pronounced decoupling: low‐fee institutions appear span the rank spectrum, whereas many high‐fee providers are not clustered at the top. This pattern challenges the assumption that prestige reliably signals value and offers stakeholders a transparent way to read price alongside position. The contribution is methodological and policy‐relevant: a tractable tool that applicants, institutions, and regulators can adopt to improve price transparency and temper ranking‐driven governance. Although designed as an exploratory case, the approach scales readily to multiple years, programmes, and realised outcomes, paving the way for evidence‐informed evaluations of value for money.

This paper introduces the Global Sensitivity Analysis framework, commonly used in mathematical modeling to assess input uncertainty, as a novel approach to understanding variable importance in machine learning. Specifically, we consider Random Forests and we aim to extend their utility beyond mere prediction. While Random Forests are highly accurate “black–box” models, their internal mechanisms often remain obscure. Traditional variable importance measures primarily quantify the contribution of each feature to predictive performance. We propose a generative variable importance ranking based on sensitivity analysis to detect the intrinsic importance of each input feature to the underlying data–generating process. As a result, it provides crucial insight into how the response is genuinely determined by the dependence structure of its predictors. A simulation study shows how our methodology not only offers deeper insights into model uncertainty but also significantly advances in explainable machine learning by enhancing explanatory capabilities and revealing complex relationships beyond just predictive performance.

Models are ruled by a politics whereby the epistemic authority borrowed from mathematics offers to modellers a considerable power to make their voice heard in the making, evaluatingand monitoring of policy. This may lead to a misuse of models, in that they are used to de-politicize issues that are political. Paradoxically, this type of political use of models is at its greatest when models can be presented as apolitical, based on pure facts and their scientific manipulation, thus veiling the normative assumptions that necessarily underpin any given modelling activity. I illustratewhat is peculiar or exceptional in the use of models with examples from various fields, including epidemiology, ecology, economics, and climate change, and reconnect this analysis with existing historical and sociological literature on quantification in general and models specifically. I also consider briefly what existing guidelines and checklists for responsiblemodelling can and cannot do, cautioning about the medium- and long-term dangers associate with model misuse.

Digital replicas (or twins) of the entire planet and of its inhabitants are being actively proposed by the research community for a variety of purposes, with a focus on climate adaptation and mitigation. Since mathematical modelling is at the core of this digital enterprise, we undertake to explore the possible limits of models in creating twins of the Earth by recalling some of the existing visions about the nature and function of mathematical models. We thus discuss what models are, what their function is in relation to the production of knowledge, and how one can question if a model is fair, by keeping the digital twins as the focus of our analysis. This leads us to discuss the way models intervene in the democratic process and orient power toward those who wield the models, and what these artifacts represent in the context of governance of science itself.