The influence of statistical information on number estimation under uncertainty: Why do people present Benford bias?

Abstract

People often have to generate numerical answers to questions they are not sure about, such as when someone has to estimate the value of an asset. The process of such estimation and how the statistical data people encounter influences it is not well understood. Recent research (e.g., Burns & Krygier, 2015) found a consistent first-digit bias that approximates the logarithm distribution of Benford’s law when individuals spontaneously generate unknown numbers, such as the lengths of rivers. They did not obtain a perfect fit to Benford’s law, but its pattern accounts for a large amount of variance in human first-digit data. Such findings were extended to other estimations using the visual stimuli of pictured items (Chi & Burns, 2022), suggesting the prevalence and robustness of this phenomenon. Thus, people exhibit a Benford bias in number generation, emphasising a stronger preference towards the smaller leading digits and a trend of monotonic decline as the first digit gets larger. Yet, the reasons behind the Benford bias remain unclear. Hence, my project examined how people acquire and utilise statistical information to shape their number estimates by exploring how easily this bias can be changed under typical experimental conditions. In four experiments, participants generated numerical estimates in response to factual questions or when assessing large quantities of visual elements. Inconsistent with the optimal statistical principles observed in everyday cognitive judgment, we have not been able to demonstrate that people’s estimation followed the underlying distribution of each variable estimated. However, supporting evidence has emerged indicating that Benford bias can be shifted through experiential learning with feedback, highlighting sensitivity to the first-digit distribution. My investigations with Benford’s law seek to enhance the framework of statistical learning and gain a better understanding of how numbers are generated for use in decision-making.