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Scientiﬁc uncertainty and decision making

It is important to have an adequate model of uncertainty, since decisions must be 
made before the uncertainty can be resolved. For instance, ﬂood defenses must be 
designed before we know the future distribution of ﬂood events. It is standardly 
assumed that probability theory oﬀers the best model of uncertain information. I 
think there are reasons to be sceptical of this claim. 
I criticise some arguments for the claim that probability theory is the only 
adequate model of uncertainty. In particular I critique Dutch book arguments, 
representation theorems, and accuracy based arguments. 
Then I put forward my preferred model: imprecise probabilities. These are sets 
of probability measures. I oﬀer several motivations for this model of uncertain 
belief, and suggest a number of interpretations of the framework. I also defend 
the model against some criticisms, including the so-called problem of dilation. 
I apply this framework to decision problems in the abstract. I discuss some 
decision rules from the literature including Levi’s E-admissibility and the more 
permissive rule favoured by Walley, among others. I then point towards some 
applications to climate decisions. My conclusions are largely negative: decision 
making under such severe uncertainty is inevitably diﬃcult. 
I ﬁnish with a case study of scientiﬁc uncertainty. Climate modellers attempt 
to oﬀer probabilistic forecasts of future climate change. There is reason to be 
sceptical that the model probabilities oﬀered really do reﬂect the chances of future 
climate change, at least at regional scales and long lead times. Indeed, scientiﬁc 
uncertainty is multi-dimensional, and diﬃcult to quantify. I argue that probability 
theory is not an adequate representation of the kinds of severe uncertainty that 
arise in some areas in science. I claim that this requires that we look for a better 
framework for modelling uncertainty