Uncertainty arises when people lack information. People’s understanding of uncertainty can play a decisive role in decision-making associated with global issues such as the financial crisis and climate change policymaking. An EU-funded project RETHINKING (Rethinking uncertainty: A problem-based approach) aimed to improve the understanding of uncertainty through a set of epistemological questions that arise with formal models of decision-making. Using an interdisciplinary approach, the work aimed at ways to resolve a fundamental problem in the field of uncertainty, namely how to identify an efficient compromise between foundational robustness and expressive power in the quantification of uncertainty. The project supports the Bayesian approach to second-order uncertainty which arises when decision-makers can (partly) model the parameters of their decision problems. The term Bayesian is derived from the 18th century mathematician and theologian Thomas Bayes. The work therefore involved choice-based semantics combined with real-valued logics, while investigating how this is related to the notion of objective probability. Objectives included using mathematical models in the social sciences and especially in economic theory in order to resolve the problems of rethinking uncertainty. A novel algebraic approach was also investigated in terms of defining conditional events. Choice-based probabilities were characterised and defined, and an analysis of their probably functions provided. Also introduced was a general framework for defining non-probabilistic measures of uncertainty as well as the extension of the classical Bayesian framework. It defined the betting criteria which lead to imprecise and non-standard probabilities. Results can have a direct impact on economic theory, the foundations of probability and statistical inference, and artificial intelligence.
Uncertainty, decision-making, Bayesianism, choice-based probabilities, economic theory