TITLE:
A General Criterion of Choice, with Discussion of Borch Paradox
AUTHORS:
Benito V. Frosini
KEYWORDS:
Utility Models, Paradoxes in Expected Utility, Risk Aversion, Borch Paradox, Mean-Variance
JOURNAL NAME:
Theoretical Economics Letters,
Vol.4 No.8,
October
22,
2014
ABSTRACT: The author resumes a proposal by Frosini of a
criterion of choice between probability prospects, which realizes a suggestion
by Allais of taking account, beside the expected utility of the dispersion or
variability of utilities. The suggested criterion is unidimensional, and is
increasing with expected utility, and decreasing, for most people, who are risk
averse, with the absolute deviation of utilities; a parameter multiplying this
dispersion measure allows for risk-averse or risk-prone behaviour, according to
its sign, and also for more or less departure from a certain prospect. This
composite criterion shares practically all desirable conditions of rationality,
and allows explaining all popular paradoxes in the literature about utility
theory. Then the author deals with an apparent, but really false paradox,
raised by Borch in connection with the representation of probability prospects
in a Markowitz-type plot. This kind of analysis is modified from the
traditional reference to points of type (mean, standard deviation) to the
reference which replaces the standard deviation with the mean absolute
deviation; no essential change is involved. The paper closes with some
numerical examples which show the correctness of the suggested criterion, as
compared to unaccettable conclusions of the expected utility approach.