Can probability theory deal with entrepreneurship?

Abstract

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”.

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Notes

  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.

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Acknowledgments

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.

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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
figure1

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.

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Tarko, V. Can probability theory deal with entrepreneurship?. Rev Austrian Econ 26, 329–345 (2013). https://doi.org/10.1007/s11138-012-0193-5

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Keywords

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

JEL Classification

  • D01
  • D83
  • D84
  • C11