Skip to main content
Log in

Knightian Uncertainty Meets Ranking Theory

  • Research Paper
  • Published:
Homo Oeconomicus Aims and scope Submit manuscript

Abstract

Knightian uncertainty is not a special kind of uncertainty; it’s just uncertainty. And it raises the issue how we may model uncertainty. The paper gives a brief overview over non-probabilistic measures of uncertainty, starting with Shackle’s functions of potential surprise and mentioning non-additive probabilities, Dempster–Shafer belief functions, etc. It arrives at an explanation of ranking theory as a further uncertainty model and emphasizes its additional epistemological virtues, which consist in a representation of belief, i.e., of taking something to be true (which is the basic notion of traditional epistemology and admits of degrees as well) and a full dynamic account of those degrees. The final section addresses the issue how these uncertainty measures and in particular ranking theory may be used within a decision theoretic context.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Carnap, R. (1971). A basic system of inductive logic, part I. In R. Carnap & R. C. Jeffrey (Eds.), Studies in inductive logic and probability (Vol. I, pp. 33–165). Berkeley: University of California Press.

    Google Scholar 

  • Choquet, G. (1953). Theory of capacities. Annales de l’Institut Fourier, 5, 131–295.

    Article  Google Scholar 

  • Cohen, L. J. (1970). The implications of induction. London: Methuen.

    Google Scholar 

  • Cohen, L. J. (1977). The probable and the provable. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Cohen, L. J. (1980). Some historical remarks on the Baconian conception of probability. Journal of the History of Ideas, 41, 219–231.

    Article  Google Scholar 

  • Dempster, A. P. (1967). Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics, 38, 325–339.

    Article  Google Scholar 

  • Dubois, D., & Prade, H. (1988). Possibility theory: An approach to computerized processing of uncertainty. New York: Plenum Press.

    Book  Google Scholar 

  • Dubois, D., Prade, H., & Sabbadin, Régis. (2001). Decision-theoretic foundations of qualitative possibility theory. European Journal of Operational Research, 128, 459–478.

    Article  Google Scholar 

  • Ellsberg, D. (1961). Risk, ambiguity, and the savage axioms. Quarterly Journal of Economies, 75, 645–669.

    Article  Google Scholar 

  • Gärdenfors, P. (1988). Knowledge in flux. Modeling the dynamics of epistemic states. Cambridge: MIT Press.

    Google Scholar 

  • Giang, P. H., & Shenoy, P. P. (2000). A qualitative linear utility theory for Spohn’s theory of epistemic beliefs. In C. Boutilier & M. Goldszmidt (Eds.), Uncertainity in artificial intelligence (Vol. 16, pp. 220–229). San Francisco: Morgan Kaufmann.

    Google Scholar 

  • Gilboa, I. (1987). Expected utility with purely subjective non-additive probabilities. Journal of Mathematical Economics, 16, 65–88.

    Article  Google Scholar 

  • Halpern, J. Y. (2003). Reasoning about uncertainty. Cambridge: MIT Press.

    Google Scholar 

  • Hild, M., & Spohn, W. (2008). The measurement of ranks and the laws of iterated contraction. Artificial Intelligence, 172, 1195–1218.

    Article  Google Scholar 

  • Hintikka, J. (1962). Knowledge and belief. Ithaca: Cornell University Press.

    Google Scholar 

  • Keynes, J. M. (1921). A treatise on probability. London: Macmillan.

    Google Scholar 

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

    Google Scholar 

  • Leitgeb, H. (2017). The stability of belief: How rational belief coheres with probability. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Levi, I. (1967). Gambling with truth. An essay on induction and the aims of science. New York: Knopf.

    Google Scholar 

  • Lewis, D. (1980). A subjectivist’s guide to objective chance. In R. C. Jeffrey (Ed.), Studies in inductive logic and probability (Vol. II, pp. 263–293). Berkeley: University of California Press.

    Google Scholar 

  • Pearl, J. (1988). Probabilistic reasoning in intelligent systems: Networks of plausible inference. San Mateo: Morgan Kaufmann.

    Google Scholar 

  • Raiffa, H. (1968). Introduction into decision analysis. Reading: Addison-Wesley.

    Google Scholar 

  • Rescher, N. (1964). Hypothetical reasoning. Amsterdam: North-Holland.

    Google Scholar 

  • Savage, L. J. (1954). The foundations of statistics. New York: Wiley. (2nd ed. in Dover 1972).

    Google Scholar 

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

    Article  Google Scholar 

  • Shackle, G. L. S. (1949). Expectation in economics. Cambridge: Cambridge University Press.

    Google Scholar 

  • Shackle, G. L. S. (1961). Decision, order, and time in human affairs. Cambridge: Cambridge University Press. (2nd ed. in 1969).

    Google Scholar 

  • Shafer, G. (1976). A mathematical theory of evidence. Princeton: Princeton University Press.

    Google Scholar 

  • Shafer, G. (1978). Non-additive probabilities in the work of Bernoulli and Lambert. Archive for History of Exact Sciences, 19, 309–370.

    Article  Google Scholar 

  • Sorensen, R. (2012). Vagueness. In Stanford encyclopedia of philosophy. https://plato.stanford.edu/entries/vagueness/.

  • Spohn, W. (1988). Ordinal conditional functions. A dynamic theory of epistemic states. In W. L. Harper & B. Skyrms (Eds.), Causation in decision, belief change, and statistics (Vol. II, pp. 105–134). Dordrecht: Kluwer.

    Chapter  Google Scholar 

  • Spohn, W. (1990). A general non-probabilistic theory of inductive reasoning. In R. D. Shachter, T. S. Levitt, J. Lemmer, & L. N. Kanal (Eds.), Uncertainty in artificial intelligence (Vol. 4, pp. 149–158). Amsterdam: Elsevier.

    Chapter  Google Scholar 

  • Spohn, W. (2012). The laws of belief. Ranking theory and its philosophical applications. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Sugeno, M. (1977). Fuzzy measures and fuzzy integrals—A survey. In M. M. Gupta et al. (Eds.), Fuzzy automata and decision processes (pp. 89–102). Amsterdam: North-Holland.

    Google Scholar 

  • Weirich, P. (2016). Causal decision theory. In Stanford encyclopedia of philosophy. https://plato.stanford.edu/entries/decision-causal/.

  • Wheeler, G. (2007). A review of the lottery paradox. In W. L. Harper & G. Wheeler (Eds.), Probability and inference: Essays in honour of Henry E. Kyburg, Jr. (pp. 1–31). London: King’s College Publications.

    Google Scholar 

  • Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3–28.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wolfgang Spohn.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Spohn, W. Knightian Uncertainty Meets Ranking Theory. Homo Oecon 34, 293–311 (2017). https://doi.org/10.1007/s41412-017-0060-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41412-017-0060-5

Keywords

JEL Classification

Navigation