# Decision making generalized by a cumulative probability weighting function

*Lindomar Soares dos Santos*,
*Natália Destefano* and
*Alexandre Souto Martinez*

*Physica A: Statistical Mechanics and its Applications*, 2018, vol. 490, issue C, 250-259

**Abstract:**
Typical examples of intertemporal decision making involve situations in which individuals must choose between a smaller reward, but more immediate, and a larger one, delivered later. Analogously, probabilistic decision making involves choices between options whose consequences differ in relation to their probability of receiving. In Economics, the expected utility theory (EUT) and the discounted utility theory (DUT) are traditionally accepted normative models for describing, respectively, probabilistic and intertemporal decision making. A large number of experiments confirmed that the linearity assumed by the EUT does not explain some observed behaviors, as nonlinear preference, risk-seeking and loss aversion. That observation led to the development of new theoretical models, called non-expected utility theories (NEUT), which include a nonlinear transformation of the probability scale. An essential feature of the so-called preference function of these theories is that the probabilities are transformed by decision weights by means of a (cumulative) probability weighting function, w(p). We obtain in this article a generalized function for the probabilistic discount process. This function has as particular cases mathematical forms already consecrated in the literature, including discount models that consider effects of psychophysical perception. We also propose a new generalized function for the functional form of w. The limiting cases of this function encompass some parametric forms already proposed in the literature. Far beyond a mere generalization, our function allows the interpretation of probabilistic decision making theories based on the assumption that individuals behave similarly in the face of probabilities and delays and is supported by phenomenological models.

**Keywords:** Utility theory; Prospect theory; Cumulative probability weighting function; Generalized functions; Complex systems (search for similar items in EconPapers)

**Date:** 2018

**References:** View references in EconPapers View complete reference list from CitEc

**Citations** Track citations by RSS feed

**Downloads:** (external link)

http://www.sciencedirect.com/science/article/pii/S037843711730746X

Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:eee:phsmap:v:490:y:2018:i:c:p:250-259

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by *K. A. Dawson*, *J. O. Indekeu*, *H.E. Stanley* and *C. Tsallis*

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier

Series data maintained by Dana Niculescu ().