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Kalai-Smorodinsky Balances for N-Tuples of Interfering Elements Read chapter Read first chapter

2017 | OriginalPaper | Chapter

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

Authors : Janusz Kacprzyk, Hannu Nurmi, Sławomir Zadrożny

Published in: Transactions on Computational Collective Intelligence XXVII

Publisher: Springer International Publishing

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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.

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previous chapter Kalai-Smorodinsky Balances for N-Tuples of Interfering Elements
next chapter A Note on Positions and Power of Players in Multicameral Voting Games
Footnotes
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
E.g. in preferences over monetary payoffs.
 
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
The argument is a slight modification of Baigent’s (1987, 163) illustration.
 
5
Admittedly, this claim rests on a specific intuitive concept of structure.
 
6
Goddard is not the first one to suggest this method. For earlier discussions, see Kendall (1955) and Brunk (1960).
 
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
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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Metadata
Title
Reason vs. Rationality: From Rankings to Tournaments in Individual Choice
Authors
Janusz Kacprzyk
Hannu Nurmi
Sławomir Zadrożny
Copyright Year
2017
Book
Transactions on Computational Collective Intelligence XXVII

Print ISBN: 978-3-319-70646-7

Electronic ISBN: 978-3-319-70647-4

Copyright Year: 2017

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

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