TITLE:
Combining Expected Utility and Weighted Gini-Simpson Index into a Non-Expected Utility Device
AUTHORS:
José Pinto Casquilho
KEYWORDS:
Non-Expected Utility, Weighted Entropies, Weighted Gini-Simpson Index, Decision Theory, Mean Contributive Value
JOURNAL NAME:
Theoretical Economics Letters,
Vol.5 No.2,
March
30,
2015
ABSTRACT: We present and discuss
a conceptual decision-making procedure supported by a mathematical device
combining expected utility and a generalized information measure: the weighted
Gini-Simpson index, linked to the scientific fields of information theory and
ecological diversity analysis. After a
synthetic review of the theoretical background relative to those themes, such a
device—an EU-WGS framework denoting a real function defined
with positive utility values and domain in the simplex of probabilities—is analytically studied, identifying its
range with focus on the maximum point, using a Lagrange multiplier method
associated with algorithms, exemplified numerically. Yet, this EU-WGS device is
showed to be a proper analog of an expected utility and weighted entropy
(EU-WE) framework recently published, both being cases of mathematical tools
that can be referred to as non-expected utility methods using decision weights,
framed within the field of decision theory linked to information theory. This
kind of decision modeling procedure can also be interpreted to be anchored in
Kurt Lewin utility’s concept and may be used to generate scenarios of optimal compositional mixtures applied to
generic lotteries associated with prospect theory, financial risk
assessment, security quantification and natural resources management. The epistemological
method followed in the reasoned choice procedure that is presented in this
paper is neither normative nor descriptive in an empirical sense, but instead
it is heuristic and hermeneutical in its conception.