Abstract
The tilted S-shaped utility function proposed in Prospect Theory (PT) relied fundamentally on the geometrical notion that there is a discontinuity between gains and losses, and that individual preferences change relative to a reference point. This results in PT having three distinct parameters; concavity, convexity and the reference point represented as a disjoint between the concavity and convexity sections of the curve. The objective of this paper is to examine the geometrical violations of PT at the zero point of reference. This qualitative study adopted a theoretical review of PT and Markowitz’s triply inflected value function concept to unravel methodological assumptions which were not fully addressed by either PT or cumulative PT. Our findings suggest a need to account for continuity and to resolve this violation of PT at the reference point. In so doing, an alternative preference transition theory, was proposed as a solution that includes a phase change space to cojoin these three separate parameters into one continuous nonlinear model. This novel conceptual model adds new knowledge of risk and uncertainty in decision making. Through a better understanding of an individual’s reference point in decision making behaviour, we add to contemporary debate by complementing empirical studies and harmonizing research in this field. Doi: 10.28991/ESJ-2022-06-01-03 Full Text: PDF
Highlights
Without providing a plausible explanation for how the reference point is derived from first principle, Prospect Theory (PT) introduced a discontinuous point between the concave segment and the convex segment in the PT curve
We examine a salient feature of the geometry of what makes one curve continuous as is exhibited in expected utility theory (EUT), and why PT is considered discontinuous
The tilted and kinked S-shaped value function curve that Kahneman and Tversky [1] proposed had a completely different geometric outlook and relied fundamentally on the concept that there is a discontinuity between gains and losses implying that preference change relative to a reference point, referred to as the status quo
Summary
Without providing a plausible explanation for how the reference point is derived from first principle, Prospect Theory (PT) introduced a discontinuous point between the concave segment (gains) and the convex segment (loses) in the PT curve. PT retained certain principles from Markowitz’s theory that was structured on EUT [1], it disagreed on other fundamental assumptions, one of which is the formulation of the reference point at the origin [3] The consensus that both theories are structured on a reference dependent platform is accepted [4, 5], but the configuration of the reference point relative to which outcomes are seen as gains and losses, is regarded as a distinct and fundamental feature in PT [6]. These are major limitations of PT [7, 8]
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