Weber-Fechner Law, Prospect Theory, and Their Data Science Applications

The article introduces the Weber-Fechner Law, a fundamental principle in psychophysics that describes the relationship between physical stimulus intensity and perceived psychological magnitude. It explains Weber's law (Δr/r = k) and Fechner's extension, which links perceived intensity to the logarithm of physical intensity, illustrating with examples such as auditory perception and sound level measurement.

Building on this, the article discusses how the Weber-Fechner Law underpins Kahneman and Tversky's Prospect Theory, a cornerstone of behavioral economics that earned a Nobel Prize. Prospect Theory posits that decision‑making involves an editing stage (forming a reference point) and an evaluation stage (assessing outcomes relative to that reference). The theory explains loss aversion and the asymmetric perception of gains versus losses.

The third part explores practical data‑science applications of these concepts at Didi. Two case studies are presented:

Application 1: Fechner’s Law in Order‑Distance Analysis – By analyzing the relationship between order distance and cancellation rate, a log‑linear pattern consistent with Fechner’s law is observed. A logistic regression model maps distance (log‑transformed) to a latent driver perception variable, allowing sensitivity analysis to guide strategies that reduce cancellations while maintaining ROI.

Application 2: Prospect Theory’s Reference Point in Strategy Evaluation – The article shows how driver perception of new dispatch strategies can be quantified using distribution skewness. Comparing skewness before and after a policy change reveals a 60% reduction in perceived bias during off‑peak periods, confirming the importance of accounting for users’ mental reference points when designing experiments.

In summary, the piece demonstrates how interdisciplinary theories from psychology and economics can be integrated with data‑driven analysis to inform product strategy, improve user experience, and support evidence‑based decision making.