Axiomatizing the Bayesian Paradigm in Parallel Small Worlds

Abstract

One of the strengths of decision analysis is that it can deal with most uncertainties; but, alas, not all. Sometimes uncertainties are too deep: that is, within the time and data currently available, no agreement is possible between decision makers, experts, and stakeholders on their quantification as probabilities. The possible range of probabilities may be so great that any sensitivity study would show that virtually all actions may be optimal. Recently, such cases have been approached by scenario-focused decision analyses in which the deep uncertainties are fixed at several “interesting” values. These approaches are showing considerable potential, but there is a problem. The assumptions on which decision analysis is based do not necessarily apply, because scenarios are not quite “small worlds” in Savage’s sense. This paper discusses the difficulty, offers a way forward, and demonstrates some of the points within an example on nuclear energy strategy.

Decision Analysis and Political Processes

“…While the decision analyses within each scenario should be coherent and rigorous, the analyses are not commensurate and directly comparable across scenarios (Stewart et al 2010, French 2014. Moreover, the scenarios do not form a spanning partition of the future; indeed, not only may some futures be missed, but also some scenarios may overlap others.…”

Decision-Making for Managing Climate-Related Risks: Unpacking the Decision Process to Avoid “Trial-and-Error” Responses

“…As such they apply in the Known and Knowable Spaces. However, the use of multiple scenarios, sensitivity analysis and exploratory decision conferences enable the methods to be applied in the Complex Space (Keeney and Raiffa, 1993;French and Rios Insua, 2000;Smith, 2010;Howard and Abbas, 2016;French, 2020;Workman et al, 2021) (See Table 3a for further details).…”

“…All can be modeled probabilistically, perhaps supplemented by sensitivity analysis (Rios Insua, 1999;Rios Insua and Ruggeri, 2000;Iooss and Saltelli, 2017). Deep uncertainties can be investigated via scenarios (French, 2020).…”

“…This may happen because data are very sparse, expert disagreements very wide or, in the case of value uncertainties, ethical issues extremely complex and controversial. In such cases, however the uncertainties should be dealt with in principle; the depth of disagreement between experts and stakeholders, the lack of data, and the need to make a decision relatively quickly mean that in practice methods that can deal with deep uncertainties will need to be adopted until the uncertainties can be resolved (Walker et al, 2013;Marchau et al, 2019;French, 2020). We discuss this further below.…”

“…Indeed, DMDU studies draw in many other approaches to decision analysis, using them to identify robust rather than optimal strategies. DMDU analyses can help decision makers to think contingently and build a more wide-ranging recognition of the risks (Walker et al, 2013;Maier et al, 2016;Marchau et al, 2019;French, 2020;Workman et al, 2021) (See Table 3b for further details).…”