Combining Expected Utility and Weighted Gini-Simpson Index into a Non-Expected Utility Device

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.