Abstract
In almost all current approaches to decision making under uncertainty, it is assumed that a decision problem is described by a set of states and set of outcomes, and the decision maker (DM) has a preference relation on a rather rich set of acts, which are functions from states to outcomes. The standard representation theorems of decision theory give conditions under which the preference relation can be represented by a utility function on outcomes and numerical representation of beliefs on states. For example, Savage [4] shows that if a DM’s preference order satisfies certain axioms, then the DM’s preference relation can be represented by a probability Pr on the state space and a utility function mapping outcomes to the reals such that she prefers act a to act b iff the expected utility of a (with respect to Pr) is greater than that of b. Moreover, the probability measure is unique and the utility function is unique up to affine transformations. Similar representations of preference can be given with respect to other representations of uncertainty (see, for example, [2,5]).
This is a short summary of a paper written with Lawrence Blume and David Easley [1]. Work supported in part by NSF under grants ITR-0325453, and IIS-0534064, by ONR under grants N00014-00-1-03-41 and N00014-01-10-511, and by the DoD Multidisciplinary University Research Initiative (MURI) program administered by the ONR under grant N00014-01-1-0795.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Blume, L., Easley, D., Halpern, J.Y.: Redoing the foundations of decision theory. In: Principles of Knowledge Representation and Reasoning: Proc. Tenth International Conference (KR 2006), pp. 14–24 (2006); A longer version, with the title “Constructive decision theory”, can be found at http://www.cs.cornell.edu/home/halpern/papers/behfinal.pdf
Gilboa, I., Schmeidler, D.: Maxmin expected utility with a non-unique prior. Journal of Mathematical Economics 18, 141–153 (1989)
Kahneman, D., Slovic, P., Tversky, A. (eds.): Judgment Under Uncertainty: Heuristics and Biases. Cambridge University Press, Cambridge (1982)
Savage, L.J.: Foundations of Statistics. Wiley, New York (1954)
Schmeidler, D.: Subjective probability and expected utility without additivity. Econometrica 57, 571–587 (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Halpern, J.Y. (2011). Constructive Decision Theory: Short Summary. In: Liu, W. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2011. Lecture Notes in Computer Science(), vol 6717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22152-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-22152-1_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22151-4
Online ISBN: 978-3-642-22152-1
eBook Packages: Computer ScienceComputer Science (R0)