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Fuzzy revealed preference theory. (English) Zbl 0536.90003

While it is widely recognised that human preferences are characterized by different degrees of indeterminacy, there have been few attempts to incorporate such nebulosity in economic theory. And these few attempts have taken the form of requiring a person’s preference to be a ’quasi- ordering’, thereby dispensing with the connectedness axiom. This paper argues that this is inadequate since a quasi-ordering has an artificial sharpness - over every pair of states it either gives a clear verdict or says nothing. There is no room for tentative judgements. A natural way of remedying this is to use the concept of a fuzzy binary relation.
It is argued that while human choices are, per force, exact, the underlying preferences which motivate these choices are often fuzzy. The standard literature on revealed preference theory as developed by Samuelson, Arrow and Richter is reinterpreted from this new perspective. Fuzzy counterparts to standard concepts are developed and several theorems established which reveal their properties. It is argued that rationality need not be a 0-1 concept and human beings may be rational of different degrees ranging from 0 to 1. It is shown that a person violating Samuelson’s Weak Axiom of Revealed Preference ’everywhere’ is totally irrational but a person violating it ’occasionally’ is rational up to a degree greater than zero but less than one.
An important aim of this paper is to develop concepts which may be useful in welfare economics in general. For instance, fuzzy preference analysis could be useful in measuring inequality, poverty, etc. It could provide an alternative to standard measures which either provide complete rankings (e.g. the Gini measure) or severely incomplete ones (e.g., the Lorenz ranking).

MSC:

91B08 Individual preferences
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
03E72 Theory of fuzzy sets, etc.
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References:

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