## 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**

- Giaquinta, M., & Hosni, H. (2015). "Mathematics in the social sciences: reflections on the theory of social choice and welfare".
*Lettera Matematica*. doi:10.1007/s40329-015-0093-1 - Flaminio, T., Godo, L., & Hosni, H. (2015) "On the algebraic structure of conditional events", In S. Destercke and T. Denoeux (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty 2015,
*Lecture Notes in Artificial Intelligence*vol. 9161, doi:10.1007/978-3-319-20807-7.

- Flaminio, T., Godo, L., & Hosni, H. (2015). "Coherence in the aggregate: A betting method for belief functions on many-valued events". International Journal of Approximate Reasoning, 58, 71–86. doi:http://dx.doi.org/10.1016/j.ijar.2015.01.001
- Flaminio, T., Godo, L. and Hosni H., (2014) "On the logical structure of de Finetti's notion of event,"
*Journal of Applied Logic,*12(3), 279–301. doi:http://dx.doi.org/10.1016/j.jal.2014.03.001

- Hosni, H and Montagna, F, (2014) "Stable Non-standard Imprecise Probabilities" In A. Laurent et al. (Ed.), IPMU 2104, Communications in Computer and Information Sciences, 444 (pp. 436–445). Springer. doi:10.1007/978-3-319-08852-5_45

- Hosni, H. (2014). "Towards a Bayesian theory of second-order uncertainty: Lessons from non-standard logics". In S. O. Hansson (Ed.), David Makinson on Classical Methods for Non-Classical Problems (pp. 195–221). Outstanding Contributions to Logic Volume 3, Springer. doi:10.1007/978-94-007-7759-0_11
- 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

**book**

- Giaquinta, M., & Hosni, H. (2015).
*Teoria della scelta sociale e Teorema fondamentale dell’economia del benessere: Razionalità, coerenza efficienza ed equità*. Edizioni della Normale.

**invited talks (selected)**

*An introduction to Bayesian Rationality,*Department of Philosophy, University of Milan, 2-5 July 2015*Rethinking the norms of rational belief and decision,*Philosophy Departmental Seminar, University of Kent, UK, 11 March 2014*Uncertain reasoning: from applications to foundations,*Interdisciplinary Techniques to reduce Uncertainty in the Sciences, Workshop, Middlesex University 24 September 2014*Is probability THE measure of uncertainty?*(w. Tommaso Flaminio) Logics for Social Behaviour, Lorenz Center, 10-14 November 2014

conference presentations (selected)

conference presentations (selected)

*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.- “Stability for non-standard imprecise probabilities” (with F. Montagna) in 15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, July 2014, Montpellier.
*Possibilistic expectation in the selection of multiple Nash equilibria*(with E. Marchioni), 11th Conference on Logic and the Foundations of Game and Decision Theory July 27-30, 2014, University of Bergen*Depth-bounded Probability Logic: A preliminary investigation (*w. M. D'Agostino and T. Flaminio) Argumentation, Rationality and Decision, Imperial College London, 18th-19th September 2014*Towards Depth-Bounded Probability Logic, http://www.uni-log.org/hunilog2015.pdf*

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