# Evaluating competing theories via a common language of qualitative verdicts

- 174 Downloads
- 2 Citations

## Abstract

Kuhn (The essential tension—Selected studies in scientific tradition and change, 1977) claimed that several algorithms can be defended to select the best theory based on epistemic values such as simplicity, accuracy, and fruitfulness. In a recent paper, Okasha (Mind 129(477):83–115, 2011) argued that no theory choice algorithm exists which satisfies a set of intuitively compelling conditions that Arrow (Social choice and individual values, 1963) had proposed for a consistent aggregation of individual preference orderings. In this paper, we put forward a solution to avoid this impossibility result. Based on previous work by Gaertner and Xu (Mathematical Social Sciences 63:193–196, 2012), we suggest to view the theory choice problem in a cardinal context and to use a general scoring function defined over a set of qualitative verdicts for every epistemic value. This aggregation method yields a complete and transitive ranking and the rule satisfies all Arrovian conditions appropriately reformulated within a cardinal setting. We also propose methods that capture the aggregation across different scientists.

### Keywords

Theory choice Social choice theory Scoring rules Thomas S. Kuhn Epistemic values## Notes

### Acknowledgments

We would like to thank an anonymous reviewer for helpful comments regarding the presentation of our overall argument. Furthermore, Claus Beisbart, Georg Brun, Kamilla Buchter, Gregory Fried, Stephan Güttinger, Paul Hoyingen-Huene, Jurgis Karpus, Simon Lohse, Alex Marcoci, James Nguyen, and Mantas Radzvilas provided fruitful feedback on earlier versions of this paper.

### Conflict of interest

The authors declare that they have no conflict of interest.

### References

- Arrow, K. J. 1963 [1951].
*Social choice and individual values*, 2nd edn. New York: John Wiley.Google Scholar - Balinski, M., & Laraki, R. (2007). A theory of measuring, electing, and ranking.
*Proceedings of the National Academy of Sciences*,*104*, 8720–8725.CrossRefGoogle Scholar - Balinski, M., & Laraki, R. (2010).
*Majority Judgment: measuring, ranking and electing*. Cambridge, MA: The MIT Press.Google Scholar - Brams, S. J., & Fishburn, P. C. (1983).
*Approval voting*. Boston: Birkhäuser.Google Scholar - Gaertner, W. (2013).
*A primer in social choice theory*. Oxford: Oxford University Press.Google Scholar - Gaertner, W., & Xu, Y. (2012). A general scoring rule.
*Mathematical Social Sciences, 63*, 193–196.Google Scholar - Hoyningen-Huene, P. (1993).
*Reconstructing scientific revolutions: Thomas S. Kuhn’s philosophy of science*(Transl. by A. T. Levine). With a foreword by Thomas S. Kuhn. Chicago: University of Chicago Press.Google Scholar - Kuhn, T. S. (1977). Objectivity, value judgment, and theory choice. In T. S. Kuhn (Ed.),
*The essential tension—Selected studies in scientific tradition and change*(pp. 320–339). Chicago: The University of Chicago Press.Google Scholar - Kuhn, T. S. 1996 [1962].
*The structure of scientific revolutions*. Chicago: The University of Chicago Press.Google Scholar - Morreau, M. (2014). Mr. Fit, Mr. simplicity and Mr. scope: From social choice to theory choice.
*Erkenntnis*,*79*, 1253–1268.CrossRefGoogle Scholar - Morreau, M. (2015). Theory choice and social choice: Kuhn vindicated.
*Mind*,*124*(493), 239–262.CrossRefGoogle Scholar - Okasha, S. (2011). Theory choice and social choice: Kuhn vs. Arrow.
*Mind*,*129*(477), 83–115.CrossRefGoogle Scholar - Pivato, M. (2014). Formal utilitarianism and range voting.
*Mathematical Social Sciences*,*67*, 50–56.CrossRefGoogle Scholar - Rizza, D. (2014). Arrow’s theorem and theory choice.
*Synthese*,*191*, 1847–1856.CrossRefGoogle Scholar - Sen, A. (1977). On weights and measures: Informational constraints in social welfare analysis.
*Econometrica*,*45*, 1539–1572.CrossRefGoogle Scholar - Sen, A. (1986). Social choice theory. In K. J. Arrow & M. D. Intriligator (Eds.),
*Handbook of mathematical economics*(Vol. 3, pp. 1073–1181). Amsterdam: North-Holland.Google Scholar - Stegenga, J. (2015). Theory choice and social choice: Okasha versus Sen.
*Mind*,*124*(493), 263–277.CrossRefGoogle Scholar - Weber, M. (2011). Experimentation versus theory choice: A social-epistemological approach. In H. B. Schmidt, D. Sirtes, & M. Weber (Eds.),
*Collective epistemology*(pp. 1–26). Frankfurt: Ontos Verlag.Google Scholar - Young, P. H. (1974). An axiomatization of Borda’s rule.
*Journal of Economic Theory*,*9*, 43–52.CrossRefGoogle Scholar