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Mathematics in the social sciences: reflections on the theory of social choice and welfare

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Lettera Matematica


This note concerns what mathematics can and cannot be expected to contribute to the social sciences and contrasts this with the contribution of mathematics to the natural sciences. Our attention is restricted to what will be termed the Central problem of social choice and welfare. Our development will be informal and space limitations will force us to gloss over a number of important questions. We refer interested readers to Giaquinta et al. (2015) for the mathematical precise details and its bibliography for the bigger picture.

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  1. Indeed, under rather mild conditions, every ordering can be represented (non-uniquely) by suitable utility functions.

  2. As anticipated above, the concept of utility is central in virtually all mathematical models in the social sciences. And yet cavalier interpretations often lead to misunderstanding which we do not have the space to prevent here. To this end, we refer the reader to [3] and in particular to Chapters 3 and 4.

  3. Think again about Euler’s equation for the motion of physical systems.

  4. Full details are available from [3].

  5. See e.g. [4].


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  2. de Finetti, B.: Un matematico e l’economia. Franco Angeli, Milano (1969)

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  3. Giaquinta, M., Hosni, H.: Teoria della scelta sociale e Teorema fondamentale dell’economia del benessere: Razionalità, coerenza efficienza ed equità. Edizioni della Normale (2015)

  4. Gigerenzer, G., Brighton, H.: Homo heuristicus: why biased minds make better inferences. Topics Cogn. Sci. 1(1), 107–143 (2009)

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  5. Pareto, V.: Manuale di Economia Politica. Società editrice libraria, Milano (1919)

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  6. Sen, A.K.: The idea of Justice. Harvard University Press (2009)

  7. von Neumann, J., Morgenstern, O.: The Theory of Games and Economic Behavior, 3rd edn. Princeton University Press, Princeton (1953)

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Correspondence to Hykel Hosni.

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Giaquinta, M., Hosni, H. Mathematics in the social sciences: reflections on the theory of social choice and welfare. Lett Mat Int 3, 101–109 (2015).

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