The Challenge

How should severe uncertainty be represented, conceptualised and reported? How should it be incorporated rationally into decision making? How is uncertainty impacted by observation and evidence — how should it be `updated’? Confidence in belief, we claim, can play a central in answering these questions.

Belief and uncertainty are in many ways two sides of the same coin. One’s rational, justifiable beliefs rein back uncertainty, just as one’s uncertainties delimit the extent and strength of one’s beliefs. A popular position has it that beliefs can be summarized by probability numbers, with 1 indicating certainty of truth, 0 certainty of falsity and numbers in between indicating various degrees of belief. It is equally, if not more popular, to summarize uncertainty, even subjective or epistemic uncertainty, by probabilities too.

But there are a range of important, pressing cases, where fully precise probabilities cannot be justifiably assigned to events of interest: be they the future economic state of a country or corporation, the precise consequences of a given CO2 emissions rate on local climate patterns, the future geo-political trajectory of the various regions of the globe. Assigning precise probability numbers in many such cases, to reflect beliefs or uncertainty, would seem quixotic; and indeed, many bodies faced with such uncertainties, from the IPCC to the US National Defense Agency, eschew such precision.

But that doesn’t mean that nothing can be said: in many of the previously cited cases, many things can be said, many previous uncertainties have been reduced, just not to the extent required by the doctrine of precise probability. When decisions are tough, and situations are important, we cannot waste even the slightest of evidence. Concluding from lack of precise probability to complete ignorance would be excessive, and destructive nihilism. The challenge, then, is to find a framework for capturing what can be believed justifiably, to what extent, and for using it to guide decision and to inform learning.

This project aims to construct such a framework around the notion of confidence in beliefs. Whilst one might not be able to make precise probability judgements – e.g. that the probability of rainfall increase in the Paris region over the next 20 years is 53% – one might be able to make interval judgements – e.g. that the probability is higher than 20%. Moreover, one can be more confident in some of these probability judgements than others. Confidence, the project aims to show, can provide a central tool for belief representation, uncertainty reporting, decision and learning. A tool that is specifically, if not uniquely, adapted for severe uncertainty.

Here are some resources relevant to the confidence-based approach.