Types of Uncertainty

Abstract

We distinguish three qualitatively different types of uncertainty—ethical, option and state space uncertainty—that are distinct from state uncertainty, the empirical uncertainty that is typically measured by a probability function on states of the world. Ethical uncertainty arises if the agent cannot assign precise utilities to consequences. Option uncertainty arises when the agent does not know what precise consequence an act has at every state. Finally, state space uncertainty exists when the agent is unsure how to construct an exhaustive state space. These types of uncertainty are characterised along three dimensions—nature, object and severity—and the relationship between them is examined. We conclude that these different forms of uncertainty cannot be reduced to empirical uncertainty about the state of the world without inducing an increase in its severity.

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Fig. 1

Notes

  1. 1.

    The program is available online at http://www.bbc.co.uk/programmes/b01hxmx1.

  2. 2.

    This is not of course to say that it is the only view being expressed. Inevitably such a broad characterisation of the state of thinking in a field will be a bit of a caricature and it is quite possible that nobody holds the default view in its completely unqualified form.

  3. 3.

    See Popper (1959) for an early statement of this argument.

  4. 4.

    Though, as Binmore (2009) emphasises, Savage only held that this applied in small-world decision making.

  5. 5.

    This epistemic reading of ambiguity aversion is not the only one to be found in the literature. See, for instance, Fox and Tversky (1995).

  6. 6.

    An argument of this kind has been made for the case of Knightian uncertainty by Bewley (1986).

  7. 7.

    See for instance Walley (1991), Joyce (2010), Bradley (2009) and Levi (1985).

  8. 8.

    The term ‘ethical’ is used here in the same way that it is used by Ramsey, to denote that which has to do with what matters to the agent. It is not meant to be read as having only to do with morality.

  9. 9.

    This is broadly the same conclusion as is reached by Broome (1991).

References

  1. Al-Najjar, N. I., & Weinstein, J. (2009). The ambiguity aversion literature: A critical assessment. Economics and Philosophy, 25, 249–284.

    Article  Google Scholar 

  2. Anscombe, F. J., & Aumann, R. J. (1963). A definition of subjective probability. The Annals of Mathematical Statistics, 34(1), 199–205.

    Article  Google Scholar 

  3. Bewley, T. F. (1986/2002). Knightian decision theory. Part I. Decisions in Economics and Finance, 25, 79–110.

    Google Scholar 

  4. Binmore, K. (2009). Rational decisions. Princeton, NJ: Princeton University Press.

    Google Scholar 

  5. Bradley, R. (2009). Revising incomplete attitudes. Synthese, 171(2), 235–256.

    Article  Google Scholar 

  6. Broome, J. (1991). Desire, belief and expectation. Mind, 100(2), 265–267.

    Article  Google Scholar 

  7. Dekel, E., Lipman, B. L., & Rustichini, A. (2001). Representing preferences with a unique subjective state space. Econometrica, 69(4), 891–934.

    Article  Google Scholar 

  8. Ellsberg, D. (1961). Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics, 75(4), 643–669.

    Article  Google Scholar 

  9. Epstein, L. G., & Seo, K. (2009). Subjective states: A more robust model. Games and Economic Behavior, 67(2), 408–427.

    Article  Google Scholar 

  10. Fox, C. R., & Tversky, A. (1995). Ambiguity aversion and comparative ignorance. The Quarterly Journal of Economics, 110(3), 585–603.

    Article  Google Scholar 

  11. Ghirardato, P. (2001). Coping with ignorance: Unforeseen contingencies and non-additive uncertainty. Economic Theory, 17, 247–276.

    Article  Google Scholar 

  12. Gilboa, I., & Schmeidler, D. (1989). Maxmin expected utility with non-unique prior. Journal of Mathematical Economics, 18, 141–153.

    Article  Google Scholar 

  13. Gilboa, I., & Schmeidler, D. (1995). Case-based decision theory. The Quarterly Journal of Economics, 110(3), 605–639.

    Article  Google Scholar 

  14. Gilboa, I., & Marinacci, M. (2011). Ambiguity and the Bayesian paradigm. Mimeo.

  15. Hansson, S.-O. (1994). Decision making under great uncertainty. Philosophy of the Social Sciences, 26(3), 369–386.

    Article  Google Scholar 

  16. Hansson, S.-O. (2013). Decision theory. A brief introduction. http://home.abe.kth.se/soh/decisiontheory.pdf.

  17. Jeffrey, R. C. (1965). The logic of decision. New York: McGraw Hill.

    Google Scholar 

  18. Joyce, J. (1999). Foundations of causal decision theory. Cambridge: Cambridge University Press.

    Google Scholar 

  19. Joyce, J. (2010). A defense of imprecise credences in inference and decision making. Philosophical Perspectives, 24(1), 281–323.

    Article  Google Scholar 

  20. Karni, E. (2013). Subjective expected utility with incomplete preferences. Econometrica, 81(1), 255–284.

    Article  Google Scholar 

  21. Keynes, J. M. (1937). The general theory of employment. The Quarterly Journal of Economics, 51(2), 2009–2023.

    Article  Google Scholar 

  22. Knight, F. H. (1921). Risk, uncertainty and profit. Boston, MA: Hart, Schaffner and Marx.

    Google Scholar 

  23. Kreps, D. M. (1992). Static choice in the presence of unforeseen contingencies. In P. Dasgupta, D. Gale, O. Hart, E. S. Maskin (Eds.), Economic analysis of markets and games (pp. 258–281). Cambridge, MA: MIT Press.

    Google Scholar 

  24. Levi, I. (1974). On indeterminate probabilities. The Journal of Philosophy, 71(13), 391–418.

    Article  Google Scholar 

  25. Levi, I. (1985). Imprecision and indeterminacy in probability judgment. Philosophy of Science, 25(3), 390–409.

    Article  Google Scholar 

  26. Levi, I. (1986). Hard choices: Decision making under unresolved conflict. Cambridge: Cambridge University Press.

    Google Scholar 

  27. Lewis, D. (1981). Causal decision theory. Australasian Journal of Philosophy, 59, 5–30.

    Article  Google Scholar 

  28. Lewis, D. (1988). Desire as belief. Mind, 97, 323–332.

    Article  Google Scholar 

  29. Luce, R. D., & Raiffa, H. (1957/1989). Games and decisions. Introduction and critical survey. New York: Dover Publications.

  30. Mas-Colell, A., Whinston, M. D., & Green, J. R. (1995). Micoreconomic theory. New York: Oxford Press.

    Google Scholar 

  31. Oddie, G. (1994). Harmony, purity, truth. Mind, 103(412), 451–472.

    Article  Google Scholar 

  32. Popper, K. (1959). The logic of scientific discovery. London: Hutchinson.

    Google Scholar 

  33. Savage, L. J. (1954). The foundations of statistics. New York: Wiley.

    Google Scholar 

  34. Schervish, M. J., Seidenfeld, T., & Kadane, J. B. (1995). A representation of partially ordered preferences. The Annals of Statistics, 23(6), 2168–2217.

    Article  Google Scholar 

  35. Schmeidler, D. (1989). Subjective probability and expected utility without additivity. Econometrica, 57(3), 571–587.

    Article  Google Scholar 

  36. Slovic, P., & Tversky, A. (1974). Who accepts Savage’s axioms?. Behavioral Science, 14, 368–373.

    Article  Google Scholar 

  37. Stalnaker, R. (1981). Letter to David Lewis. In W. Harper, Stalnaker & G. Pearce & (Eds.), IFS: Conditionals, belief, decision, chance, and time. Dordrecht, NL: Reidel.

    Google Scholar 

  38. Walker, O., & Dietz, S. (2011). A representation result for choice under conscious unawareness. Working Paper, Grantham Research Institute, London, UK.

  39. Walley, P. (1991). Statistical reasoning with imprecise probabilities. London: Chapman and Hall.

    Google Scholar 

  40. Weintraub, R. (2007). Desire as belief, Lewis notwithstanding. Logic and Analysis, 67(294), 116–122.

    Article  Google Scholar 

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Acknowledgements

We would like to acknowledge the support of the Arts and Humanities Research Council (Grant Reference: AH/I003118/1), The Netherlands Organisation for Scientific Research (Grant Number 236-20-005), and the Fonds National de la Recherche Luxembourg (Grant Number 09-194). We are grateful to Hykel Hosni and Casey Helgeson for their comments on an earlier draft.

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Correspondence to Mareile Drechsler.

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Bradley, R., Drechsler, M. Types of Uncertainty. Erkenn 79, 1225–1248 (2014). https://doi.org/10.1007/s10670-013-9518-4

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Keywords

  • Factual Uncertainty
  • Normative Uncertainty
  • Causal Decision Theorist
  • Evidential Decision Theory
  • Default View