Vol. 2 (2023)
Issue 4 (December) 10.58567/eal02040005
The gap between formalism and empirical science: the example of the non-dictatorship condition
School of Business and Creative Industries, University of the Sunshine Coast, Sippy Downs, Australia
Author to whom correspondence should be addressed.
Received: 12 June 2023 / Accepted: 18 July 2023 / Published: 7 August 2023
Since the establishment of neoclassical economics in the nineteenth century, there has been a debate in the economics profession over the role played by mathematics. Mathematics can add precision to discussion of real-world empirical problems in economics, but care needs to be taken when formalizing a problem to ensure that errors of translation are not made. Formalism allows one to be sure that a chain of reasoning is correct but applying conclusions back to an empirical science problem is fraught if an error of translation has been made. We illustrate such a difficulty in the context of Arrow’s impossibility theorem, specifically the mistranslation of the non-dictatorship condition. The notion of dictatorship entails causality, but causality does not correspond to the usage of the implication sign in mathematics or logic. We use the rules of logic to illustrate that the way that dictatorship is rendered mathematically in the impossibility theorem makes the existence of a dictator (or dictators) not only reasonable but likely.
© 2023 by J. Alexander. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) (
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J. Alexander, W. R. The gap between formalism and empirical science: the example of the non-dictatorship condition.
Economic Analysis Letters, 2023, 2, 39. https://doi.org/10.58567/eal02040005
J. Alexander W R. The gap between formalism and empirical science: the example of the non-dictatorship condition.
Economic Analysis Letters; 2023, 2(4):39. https://doi.org/10.58567/eal02040005
J. Alexander, W. R. 2023. "The gap between formalism and empirical science: the example of the non-dictatorship condition"
Economic Analysis Letters 2, no.4: 39. https://doi.org/10.58567/eal02040005
J. Alexander, W. R. (2023). The gap between formalism and empirical science: the example of the non-dictatorship condition.
Economic Analysis Letters, 2(4), 39. https://doi.org/10.58567/eal02040005
Article Access Statistics
Arrow, K. J. (1950). A difficulty in the concept of social welfare. Journal of Political Economy, 58, 328-346. https://doi.org/10.1086/256963
Arrow, K. J. (1983). Collected papers of Kenneth J. Arrow: Social choice and justice. Harvard University Press. https://www.hup.harvard.edu/catalog.php?isbn=9780674137608&content=toc
Bronfenbrenner, M. (1991). Economics as dentistry. Southern Economic Journal, 57, 599-605. https://www.jstor.org/stable/i243581
Crespo, R. & Tohmé, F. (2017). The future of mathematics in economics: a philosophically grounded proposal. Foundations of Science, 22, 677-693. https://doi.org/10.1007/s10699-016-9492-9
Hahn, F. H. (1970). Some adjustment problems. Econometrica, 38, 1-17. https://www.econometricsociety.org/publications/econometrica/1970/01/01/some-adjustment-problems
Leontief, W. (1971). Theoretical assumptions and nonobserved facts. American Economic Review, 61, 1-7. https://www.jstor.org/stable/i332664
Little, I. M. D. (1952). Social choice and individual values. Journal of Political Economy, 60, 422-432. https://doi.org/10.1086/257276
Lucas, R. E., JR. (1981). Studies in Business-Cycle Theory, Cambridge, Mass, The MIT Press.
Mackay, A. F. (1981). Arrow's theorem: The paradox of social choice. British Journal for the Philosophy of Science, 32.
Mayer, T. (1993). Truth versus precision in economics, E. Elgar.
Phelps Brown, E. (1972). The underdevelopment of economics. The Economic Journal, 82, 1-10. https://doi.org/10.2307/2230254
Pigou, A. C. E. (1925). Memorials of Alfred Marshall, Macmillan and Company, limited.