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Transactions on Computational Collective Intelligence XXVII pp 28–39Cite as

Reason vs. Rationality: From Rankings to Tournaments in Individual Choice

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Part of the book series: Lecture Notes in Computer Science ((TCCI,volume 10480))

Abstract

The standard assumption in decision theory, microeconomics and social choice is that individuals (consumers, voters) are endowed with preferences that can be expressed as complete and transitive binary relations over alternatives (bundles of goods, policies, candidates). While this may often be the case, we show by way of toy examples that incomplete and intransitive preference relations are not only conceivable, but make intuitive sense. We then suggest that fuzzy preference relations and solution concepts based on them are plausible in accommodating those features that give rise to intransitive and incomplete preferences. Tracing the history of those solutions leads to the works of Zermelo in 1920’s.

The authors are grateful to the referees for perceptive and constructive comments on an earlier version.

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Notes

  1. 1.

    The weak preference of A over B means that A is regarded as at least as desirable as B. Thus the weak preference relation is not asymmetric, while the strong one is.

  2. 2.

    E.g. in preferences over monetary payoffs.

  3. 3.

    All preferences underlying the table are assumed to be strict. The composition of the advisory body may raise some eyebrows. So, instead of these particular categories of advisors, one may simply think of a body that consists of three peers.

  4. 4.

    The argument is a slight modification of Baigent’s (1987, 163) illustration.

  5. 5.

    Admittedly, this claim rests on a specific intuitive concept of structure.

  6. 6.

    Goddard is not the first one to suggest this method. For earlier discussions, see Kendall (1955) and Brunk (1960).

  7. 7.

    The differences between Zermelo’s and Goddard’s approaches are cogently analyzed by Stob (1985). Much of what is said in this and the next paragraph is based on Stob’s brief note.

  8. 8.

    We shall here ignore the ties in pairwise comparisons. These can certainly be dealt with in fuzzy systems theory. Also the tournament literature referred to here is capable of handling them. Ties are typically considered as half-victories, i.e. given a value 1/2 in the tournament matrices.

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Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk & Sławomir Zadrożny

  2. Department of Philosophy, Contemporary History and Political Science, University of Turku, Turku, Finland

    Hannu Nurmi

Authors
  1. Janusz Kacprzyk
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  2. Hannu Nurmi
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  3. Sławomir Zadrożny
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Correspondence to Hannu Nurmi .

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Editors and Affiliations

  1. Department of Finance and Management, The WSB University, Wroclaw, Poland

    Jacek Mercik

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Kacprzyk, J., Nurmi, H., Zadrożny, S. (2017). Reason vs. Rationality: From Rankings to Tournaments in Individual Choice. In: Mercik, J. (eds) Transactions on Computational Collective Intelligence XXVII. Lecture Notes in Computer Science(), vol 10480. Springer, Cham. https://doi.org/10.1007/978-3-319-70647-4_2

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  • DOI: https://doi.org/10.1007/978-3-319-70647-4_2

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