Abstract
Software agents and humans alike face severe difficulties in making decisions in uncertain contexts. One approach is to formalise the decision situation by means of decision theory, i.e. probabilities and utilities leading to the principle of maximising the expected utility. Expected utility is here considered as a stochastic variable; under the assumption that all utility values are equally likely, and that each vector of probability values is equally likely, the probability distribution of expected utility is calculated for two, three, and four possible outcomes. The effect of these probability distributions concentrating around the middle value is explored and its significance for making decisions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131–295 (1954)
DeConcini, C., Procesi, C.: The algebra of the box spline (2006), http://www.citebase.org/abstract?id=oai:arXiv.org:math/0602019
Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics xxxviii, 325–399 (1967)
Ekenberg, L., Thorbiörnson, J.: Second-order decision analysis. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 9(1), 13–38 (2001)
Huber, P.J.: The case of choquet capacities in statistics. Bulletin of the International Statistical Institute 45, 181–188 (1973)
Huber, P.J., Strassen, V.: Minimax tests and the neyman-pearsons lemma for capacities. Annals of Statistics 1, 251–263 (1973)
Lewin, L.: Polylogarithms and Associated Functions. North-Holland, Amsterdam (1981)
Nau, R.F.: Uncertainty aversion with second-order utilities and probabilities. Management Science 52(1), 136–145 (2006)
Shafer, G.: A Mathematical theory of evidence. Princeton University Press, Princeton (1976)
Shapira, Z.: Risk Taking: A Managerial Perspective. Russel Sage Foundation, Thousand Oaks (1995)
Sundgren, D., Danielson, M., Ekenberg, L.: Some second order effects on interval based probabilities. In: Proceedings of the Nineteenth International Florida Artificial Intelligence Research Society Conference, pp. 848–853. AAAI Press, Menlo Park (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sundgren, D., Ekenberg, L., Danielson, M. (2008). Some Properties of Aggregated Distributions over Expected Values. In: Gelbukh, A., Morales, E.F. (eds) MICAI 2008: Advances in Artificial Intelligence. MICAI 2008. Lecture Notes in Computer Science(), vol 5317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88636-5_66
Download citation
DOI: https://doi.org/10.1007/978-3-540-88636-5_66
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88635-8
Online ISBN: 978-3-540-88636-5
eBook Packages: Computer ScienceComputer Science (R0)