## Re-thinking uncertanty: A choice-based approach

The overarching aim of this research project is to improve our understanding of uncertainty, its quantification and its communication. It sets out to do so by addressing a set of key epistemological questions that arise in the construction of formal models of rational decision- making. Its expected results will throw new light one of the most fundamental problems in the multidisciplinary field of uncertain reasoning: How to identify an efficient trade-off between foundational robustness and expressive power in the quantification of uncertainty.

Our need to quantify uncertainty arises primarily in relation to choice problems, i.e. when we must select one from a set of alternatives each yielding a (partially) unknown outcome. Yet, some choice problems lead to an easier quantification of the related uncertainty than others. Suppose a normal-looking die is about to be rolled. In the absence of other relevant information it is entirely plausible to believe that a particular side, say “3”, will show with probability 1/6. The underlying reasoning goes along the following lines: The problem at hand clearly admits of six mutually exclusive outcomes, one of which will certainly occur, and none of which appears to be more likely than the others – hence it would seem irrational of us to give a particular side a probability other than 1/6. Compare this with a situation in which we must decide whether to buy stocks of a certain bank who has invested heavily in Greek bonds. We are told that in the event of Greece exiting the Eurozone, Greek bonds will be completely worthless. Yet the stocks offer very good prospects of profit in a six-month time horizon. In order to make a rational decision we must estimate the likelihood (i.e. choose a representation for our uncertainty) that Greece will exit the Eurozone within the next six months – an event which is often referred to as “GREXIT” in the financial sector. The reasoning we confidently used to choose our probability for the event “3 by rolling a normal-looking die” certainly doesn’t seem to be applicable to GREXIT. In particular there seems no unique way of telling a priori what set should be partitioned in order to define a standard probability distribution.

**Background**Our need to quantify uncertainty arises primarily in relation to choice problems, i.e. when we must select one from a set of alternatives each yielding a (partially) unknown outcome. Yet, some choice problems lead to an easier quantification of the related uncertainty than others. Suppose a normal-looking die is about to be rolled. In the absence of other relevant information it is entirely plausible to believe that a particular side, say “3”, will show with probability 1/6. The underlying reasoning goes along the following lines: The problem at hand clearly admits of six mutually exclusive outcomes, one of which will certainly occur, and none of which appears to be more likely than the others – hence it would seem irrational of us to give a particular side a probability other than 1/6. Compare this with a situation in which we must decide whether to buy stocks of a certain bank who has invested heavily in Greek bonds. We are told that in the event of Greece exiting the Eurozone, Greek bonds will be completely worthless. Yet the stocks offer very good prospects of profit in a six-month time horizon. In order to make a rational decision we must estimate the likelihood (i.e. choose a representation for our uncertainty) that Greece will exit the Eurozone within the next six months – an event which is often referred to as “GREXIT” in the financial sector. The reasoning we confidently used to choose our probability for the event “3 by rolling a normal-looking die” certainly doesn’t seem to be applicable to GREXIT. In particular there seems no unique way of telling a priori what set should be partitioned in order to define a standard probability distribution.

This project is funded by the European Commission under the Marie Curie IEF-GA-2012-327630 project

*Rethinking Uncertainty,*and it is part of the LSE's Managing Severe Uncertainty project.

## output

**articles**

- Flaminio, T., Godo, L. and Hosni H., (2014) On the logical structure of de Finetti's notion of event,
*Journal of Applied Logic,*forthcoming. - Hosni, H and Montagna, F, (2014)
*Stable Non-standard Imprecise Probabilities*, submitted for conference proceedings publication. - Flaminio, T., Godo, L. and Hosni, H. (2013)
*Zero-probability and coherent betting: a logical point of view.*In: Symbolic and quantiative approaches to resoning with uncertainty. Lecture notes in artificial intelligence (7958). Springer, Utrecht, The Netherland, pp. 206-217. ISBN 9783642390913

invited talks

invited talks

*Rethinking the norms of rational belief and decision,*Philosophy Departmental Seminar, University of Kent, UK, 11 March 2014

conference presentations

conference presentations

*On the logical structure of de Finetti's notion of event,*in Combining Probability and Logic, Munich Centre for Mathematical Philosophy, September 2013*Rethinking Uncertainty: Some Key Questions*, in 35th Linz Seminar on Fuzzy Set Theory "Graded logical approaches and their applications", Linz, 18-22 February 2014. Abstract.

what's hot in uncertain reasoning

what's hot in uncertain reasoning

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**organising / impact / outreach**

*Una giornata per la matematica, Scuola Normale Superiore, Pisa 14.3.14*- AILA 2014, Scuola Normale Superiore, Pisa 14-17.4.14
- Games and Decisions 2, Scuola Normale Superiore, Pisa, 7-9.7.14