Can probability theory deal with entrepreneurship?


The Austrian theory of entrepreneurship emphasizes the importance of epistemic heterogeneity and the unlistability of the set of all possibilities. A similar concern with what has been called “the art of choosing the space of possibilities” is an important part of Bayesian model selection. Both Austrian and Bayesian authors view the common knowledge assumption as an unrealistic and unnecessary restriction. This coincidence of concerns leads to a joint theory of entrepreneurship. Three important benefits result from this merger: (1) the ability to use Itti & Baldi’s Bayesian theory of surprise to empirically measure radical surprise and improve the Betrand competition model as a consequence, (2) dealing with the unlistability problem, and (3) better understanding why the emergence of common knowledge is always the outcome of a social process rather than an inherent consequence of “rationality”.

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


  1. 1.

    The logarithm is taken in base 2 in order to measure the quantity of information in bits.

  2. 2.

    The three steps are not necessarily performed by the same person within the firm (e.g. the manager). For example, step (1) may be made within either the R&D or the marketing department, step (2) is a managerial task per se, and step (3) is an entrepreneurial task most closely associated to the owners of the firm.

  3. 3.

    although even this is can be doubted in the light of the heuristics literature (Gigerenzer et al. 1999)

  4. 4.

    The rigorous form of Bayes’ formula is the following: \( p\left( {\left. x \right|I,X} \right)={{{p\left( {\left. x \right|X} \right)p\left( {\left. I \right|x,X} \right)}} \left/ {{p\left( {\left. I \right|X} \right)}} \right.} \). However, it is often written in abbreviated form as \( p\left( {\left. x \right|I,X} \right)={{{p(x)p\left( {\left. I \right|x} \right)}} \left/ {p(I) } \right.} \), which masks to some extent the subjectivity involved, in particular it creates the illusion that the likelihood, p(I|x, X), doesn’t depend on one’s background assumptions X, but describes instead an objective relation between the new data I and the variable of interest x.


  1. Boettke, P. J. (1998). Rational choice and human agency in economics and sociology: Exploring the Weber-Austrian connection. In H. Giersch (Ed.), Merits and limits of markets (pp. 53–81). Berlin: Springer.

  2. Boettke, P. J., & Coyne, C. J. (2009). An entrepreneurial theory of social cultural change. In V. P. Díaz (Ed.), Markets and civil society: The European experience in comparative perspective (pp. 77–103). New York: Berghahn Books.

  3. Bretthorst, G. L. (1988). Bayesian spectrum analysis and parameter estimation. Berlin: Springer-Verlag.

  4. Bretthorst, G. L. (1990). An introduction to parameter estimation using Bayesian probability theory. In P. F. Fougère (Ed.), Maximum-entropy and Bayesian methods (pp. 53–79). Dordrecht, Netherlands: Kluwer Academic Publishers.

  5. Bretthorst, G. L. (1996). An introduction to model selection using probability theory as logic. In G. Heidbreder (Ed.), Maximum entropy and Bayesian methods (pp. 1–42). Dordrecht, Netherlands: Kluwer Academic Publishers.

  6. Caplan, B. (1999). The Austrian search for realistic foundations. Southern Economic Journal, 65(4), 823–838.

    Article  Google Scholar 

  7. Caplan, B. (2001). Probability, common sense, and realism: a reply to Huelsmann and Block. Quarterly Journal of Austrian Economics, 4(2), 69–86.

    Google Scholar 

  8. Clarke, K. A., & Primo, D. M. (2012). A model discipline: Political science and the logic of representations. Oxford: Oxford University Press.

  9. Cowen, T., & Hanson, R. (2007). Are disagreements honest? Working Paper, George Mason University, Mercatus Center.

  10. Crovelli, M. R. (2009). On the possibility of assigning probabilities to singular cases, or: probability is subjective too! Libertarian Papers, 1(26).

  11. Gigerenzer, G., Todd, P. M., The ABC Research Group. (1999). Simple heuristics that make us smart. Oxford: Oxford University Press.

  12. Gull, S. F. (1988). Bayesian inductive inference and maximum entropy. In G. J. Erickson & C. R. Smith (Eds.), Maximum-entropy and Bayesian methods in science and engineering, vol. 1: Foundations (pp. 53–74). Dordrecht: Kluwer.

    Google Scholar 

  13. Hayek, F. (1952). The counter-revolution of science: Studies on the abuse of reason. Glencoe, Illinois: Free Press.

  14. Headd, B. (2003). Redefining business success: distinguishing between closure and failure. Small Business Economics, 21(1), 51–61.

    Article  Google Scholar 

  15. Hirshleifer, J. (1970). Investment, interest, and capital. New Jersey: Prentice-Hall.

  16. Hubbard, D. W. (2010). How to measure anything: Finding the value of intangibles in business (2nd ed.). New Jersey: John Wiley & Sons.

  17. Itti, L., & Baldi, P. F. (2005). A principled approach to detecting surprising events in video. Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1, 631–637.

    Google Scholar 

  18. Itti, L., & Baldi, P. F. (2006). Bayesian surprise attracts human attention. In Advances in neural information processing systems, vol. 19 (pp. 547–554). Cambridge, MA: MIT Press.

  19. Jaynes, E. (1985). Entropy and search-theory. In C. R. Smith & W. T. Grandy Jr. (Eds.), Maximum-entropy and Bayesian methods in inverse problems (pp. 443–454). Dordrecht, Netherlands: D. Reidel Publishing Company.

  20. Jaynes, E. (1986). Bayesian methods: General background. In J. H. Justice (Ed.), Maximum-entropy and Bayesian methods in applied statistics (pp. 1–25). Cambridge: Cambridge University Press.

  21. Jaynes, E. (1988). How does the brain do plausible reasoning. In G. J. Erickson & C. R. Smith (Eds.), Maximum-entropy and Bayesian methods in science and engineering, vol. 1. Foundations (pp. 1–24). Dordrecht, Netherlands: Kluwer Academic Publishing.

  22. Jaynes, E. (2003). Probability theory: The logic of science. Cambridge: Cambridge University Press.

    Google Scholar 

  23. Jeffreys, H. (1961). Theory of probability (3rd ed.). Oxford: Oxford University Press.

  24. Jensen, F. V., & Nielsen, T. D. (2007). Bayesian networks and decision graphs (2nd ed.). Berlin: Springer.

  25. Kass, R. E., & Wasserman, L. (1996). The selection of prior distributions by formal rules. Journal of the American Statistical Association, 91(435), 1343–1370.

    Article  Google Scholar 

  26. Keynes, J. M. (1921). A treatise on probability. London: Macmillan And Co.

  27. Kirzner, I. (1973). Competition and entrepreneurship. Chicago: University of Chicago Press.

  28. Kirzner, I. (1976). Equilibrium versus market process. In E. G. Dolan (Ed.), The foundations of modern Austrian economics. Kansas: Sheed and Ward.

  29. Kirzner, I. (1980). Perception, opportunity and profit: Studies in the theory of entrepreneurship. Chicago: University of Chicago Press.

  30. Kirzner, I. M. (1997). Entrepreneurial discovery and the competitive market process: an Austrian approach. Journal of Economic Literature, 35(1), 60–85.

    Google Scholar 

  31. Klein, D. B. (2012). Knowledge and coordination. Oxford: Oxford University Press.

  32. Knaup, A. E. (2005). Survival and longevity in the business employment dynamics data. Monthly Labor Review, 5, 50–56.

    Google Scholar 

  33. Knight, F. H. (1921). Risk, uncertainty, and profit. Cambridge: Houghton Mifflin Company, The Riverside Press.

  34. Lachmann, L. M. (1976). On the central concept of Austrian economics: Market process. In E. G. Dolan (Ed.), The foundations of modern Austrian economics. Kansas: Sheed and Ward.

  35. Langlois, R. N. (1982a). Subjective probability and subjective economics. R.R. #82-09, New York University, C.V. Starr Center for Applied Economics.

  36. Langlois, R. N. (1982b). Entrepreneurship and knowledge. R.R. #82-13, New York University, C.V. Starr Center for Applied Economics.

  37. Laplace, P. S. (1840 [1951]). A philosophical essay on probabilities (6th ed.). (F. W. Truscott, & F. L. Emory, Trans.) Dover.

  38. Lucas, R. E. (1977). Understanding business cycles. Carnegie-Rochester Conference Series on Public Policy, 5, 7–29.

    Article  Google Scholar 

  39. Milgrom, P., & Stokey, N. (1982). Information, trade and common knowledge. Journal of Economic Theory, 26(1), 17–27.

    Article  Google Scholar 

  40. Mises, L. (1996 [1949]). Human action: A treatise on economics (4th ed.). San Francisco: Fox & Wilkes.

  41. Mises, L. (1957 [2007]). Theory and history. Auburn, Alabama: Ludwig von Mises Institute.

  42. O’Driscoll Jr., G. P., & Rizzo, M. (1985). The economics of time and ignorance. Oxford: Blackwell.

  43. Phillips, L. D. (1970). The ‘true probability’ problem. Acta Psychologica, 34, 254–264.

    Article  Google Scholar 

  44. Romer, P. (1993). Economic growth. In D. R. Henderson (Ed.), The concise encyclopedia of economics. Indianapolis, IN: Liberty Fund, Inc.

  45. Samuelson, L. (2004). Modeling knowledge in economic analysis. Journal of Economic Literature, 42(2), 367–403.

    Article  Google Scholar 

  46. Sarasvathy, S. D. (2001). Causation and effectuation: toward a theoretical shift from economic inevitability to entrepreneurial contingency. Academy of Management Review, 26(2), 243–288.

    Google Scholar 

  47. Sarasvathy, S. D. (2003). Entrepreneurship as a science of the artificial. Journal of Economic Psychology, 24(2), 203–220.

    Article  Google Scholar 

  48. Sarasvathy, S. D., & Dew, N. (2007). Without judgment: An empirically-based entrepreneurial theory of the firm. Working Paper 84, George Mason University, Mercatus Center.

  49. Schutjens, V., & Stam, E. (2006). Starting anew: Entrepreneurial intentions and realizations subsequent to business closure. Research Paper ERS-2006-015-ORG, Erasmus Research Institute of Management.

  50. Shane, S. A. (2008). The illusions of entrepreneurship: The costly myths that entrepreneurs, investors, and policy makers live by. New Haven & London: Yale University Press.

  51. Suppes, P. (1986). Probabilistic metaphysics. Oxford: Blackwell.

  52. Vosniadou, S., & Ortony, A. (Eds.). (1989). Similarity and analogical reasoning. Cambridge: Cambridge University Press.

  53. Wu, B., & Knott, A. M. (2006). Entrepreneurial risk and market entry. Management Science, 52(9), 1315–1330.

    Article  Google Scholar 

Download references


I have received very useful feedback on earlier versions of the paper from Dragos Paul Aligica, Simon Bilo, Peter Boettke, Bryan Caplan, Robert Cavender, Chris Coyne, Thomas Duncan, Jesse Gastelle, Laura Grube, Dave Hebert, Ryan Langrill, Peter Leeson, Jayme Lemke, William Luther, Lotta Moberg, Kyle O’Donnell, Shruti Rajagopalan, Alexander Salter, Solomon Stein, Virgill Storr, Jessi Troyan, and an anonymous reviewer.

Author information



Corresponding author

Correspondence to Vlad Tarko.

Annex: probability assignments and background assumptions

Annex: probability assignments and background assumptions

This annex provides a simple example illustrating (1) that different background assumptions lead to different probability assignments of the same event, and (2) the rational expectations prediction is inferior to the general Bayesian method.

Suppose we have a die with an unknown number of sides, and we know from a series of throws that “1” has appeared once, “2” five times, and “3” four times (this is our data). From a rational expectations perspective, the probability distribution is \( p(x)=\frac{n_x }{n} \), where n x is the number of times x happened, and n is the total number of draws (1 + 5 + 4 = 10). By contrast, from a Bayesian perspective, which incorporates all kinds of information, we know, first of all, that the die, as a three-dimensional object, has to have at least four sides. Furthermore, when we start with the principle of indifference assumption of equal prior probabilities, and we then update using Bayes formula and the given data, we arrive at Laplace’s rule of succession: \( p(x)=\frac{{n_x +1}}{n+N } \), where N is the assumed total number of sides (Jaynes 2003: eq. 18.44). The comparative results are presented in Table 1 and Fig. 1.

Table 1 Probability Estimates from the Same Empirical Data Under Different Theoretical Assumptions
Fig. 1

Probability Estimates from the Same Empirical Data Under Different Theoretical Assumptions.

As it should be obvious, the Bayesian answers are superior to the rational expectations answer because the rational expectations answer assumes something which is not actually given, namely that it is impossible for side 4 to happen anytime in the future. The rational expectations perspective effectively bans us from taking into consideration the relevant information that we’re dealing with a three-dimensional object.

Moreover, the different Bayesian predictions, relying on different assumptions about N, highlight that the exact numeric values of the probability distribution, even in this case of a repeated experiment under homogenous conditions, critically depend on our theoretical assumption about the set of possibilities. Given that such complications appear even in the simplest examples, we see why Bayesians emphasize that there’s no escape from the conditional nature of all probabilities.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Tarko, V. Can probability theory deal with entrepreneurship?. Rev Austrian Econ 26, 329–345 (2013).

Download citation


  • Kiznerian entrepreneurship
  • Bayesian surprise
  • Unknown unknowns
  • Radical uncertainty
  • Bertrand competition

JEL Classification

  • D01
  • D83
  • D84
  • C11