3 research outputs found
Scientiļ¬c 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, ļ¬ood defenses must be
designed before we know the future distribution of ļ¬ood events. It is standardly
assumed that probability theory oļ¬ers 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 oļ¬er 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 Leviās 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 diļ¬cult.
I ļ¬nish with a case study of scientiļ¬c uncertainty. Climate modellers attempt
to oļ¬er probabilistic forecasts of future climate change. There is reason to be
sceptical that the model probabilities oļ¬ered really do reļ¬ect the chances of future
climate change, at least at regional scales and long lead times. Indeed, scientiļ¬c
uncertainty is multi-dimensional, and diļ¬cult 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 uncertaint
Extendibility of choquet rational preferences on generalized lotteries
Given a finite set of generalized lotteries, that is random quantities equipped with a belief function, and a partial preference relation on them, a necessary and sufficient condition (Choquet rationality) has been provided for its representation as a Choquet expected utility of a strictly increasing utility function. Here we prove that this condition assures the extension of the preference relation and it actually guides the decision maker in this process