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Representations of Preferences Orderings (Paperback, 1995 ed.)
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Representations of Preferences Orderings (Paperback, 1995 ed.)
Series: Lecture Notes in Economics and Mathematical Systems, 422
Expected to ship within 10 - 15 working days
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A basic assumption made by pioneers of classical microeconomics
such as Edgeworth and Pareto was that the ranking of a consumer's
preferences could always be measured numerically, by associating to
each possible con- sumption bundle a real number that measured its
utility: the greater the utility, the more preferred was the
bundle, and conversely. It took several decades before the naivety
of this assumption was seriously challenged by economists, such as
Wold, attempting to find conditions under which it could be
justified mathematically. Wold's work was the first in a long chain
of results of that type, leading to the definitive theorems of
Debreu and oth- ers in the 1960s, and subsequently to the
refinements and generalisations that have appeared in the last
twenty-five years. Out of this historical background there has
appeared a general mathe- matical problem which, as well as having
applications in economics, psy- chology, and measurement theory,
arises naturally in the study of sets bear- ing order relations:
Given some kind of ordenng t on a set 5, fina a real-valued mapping
u on 5 such that for any elements x, y of 5, x t yif and only if
u(x) 2: u(y). If also 5 has a topology (respective/y, differential
structure), find conditions that ensure the continuity
(respectively, differentiability) of the mapping u. A mapping *u of
this kind is called a representation of the ordering C:::.
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