A Novel Probability Weighting Function Model with Empirical Studies

Abstract

Probability weighting is one of the key components of the modern risky decision-making theories, an effective probability weight function can more accurately describe the decision-makers' subjective response to the event probability. While the probability weighting functions (PWFs) with several different parametric forms and parameter-free elicitation methods have been proposed. This paper first introduces a Lagrange interpolation method (LIM) for building a parameter-free PWF model, then proposes a novel PWF model with the use of the LIM based on Prelec's PWF model. Furthermore, an experiment was designed and carried out. The results not only demonstrate that the novel PWF model could reflect the empirical regularities for maximizing the satisfaction degree of the curve fitting for the preference points obtained from experiment or questionnaire survey and better predict the preferences of decision-makers, but also are found to be consistent with the properties of PWF. This paper makes a significant methodological contribution to developing a numerical method, such as LIM, for constructing the probability weighting model. The finial error analysis suggests that the novel PWF model is a more effective approach.

Keywords

• Probability weighting function
• Decision-making under risk
• Lagrange interpolation method
• Risk preference
• Preference points
• Empirical studies