Master's thesis, School of Psychology, University of Sydney.

**ISSN/ISBN:** Not available at this time.
**DOI:** Not available at this time.

- For online information, click here.

**Abstract:** Decision making under uncertainty has been investigated by looking for regularities due to the application of heuristics (Tversky & Kahneman, 1974). Contemporary society demands that we estimate numbers when making decisions, for instance, the value of an item, so regularities in the numbers people generate could help us understand how humans deal with unknown situations. Recent research (e.g., Burns, 2009) suggests that people could spontaneously exhibit a stronger bias towards the smaller leading digits (e.g., 1, 2) that approximates Benford’s law, a well-established phenomenon of the first digits aggregated from the naturally occurring datasets. Hence, it may also represent a potential regularity in how people produce unknown numbers. Therefore, the present study attempted to investigate the conditions under which the first digit phenomenon might occur under uncertainty by examining the degree of fit to Benford’s law with various forms of numerical responses, and more importantly, testing the existing speculations of why people might present such a bias when generating unknown values. The key elements of the designs were the statements of numerical questions and simple visual displays for estimations. As expected, the first digit phenomenon was stronger when generating non-arbitrary numbers, compared to the arbitrary numbers. The critical findings were the extension of Benford’s law to the estimation tasks
with a peak of digit-5; the continued failure of the recognition hypothesis as a reliable explanation; and the supporting evidence
of the Integration Hypothesis, which emphasises the attribute of processing multiple information for the occurrence of the first digit phenomenon in number generation. Building on and extending the results of the previous research conducted, the outcomes of this project can assist in understanding: 1) how numerical responses to unknown questions inform theories of numerical cognition and decision making, and 2) how the pattern of leading digits generated from humans might offer implications for the practices of Benford’s law in fraud detection.

**Bibtex:**

```
@thesis{,
author = {Duyi Chi},
title = {First Digit Phenomenon in Number Generation Under Uncertainty: Through the Lens of Benford’s Law},
year = {2020},
institution = {University of Sydney},
url = {https://ses.library.usyd.edu.au/bitstream/handle/2123/22422/Chi_D_Thesis.pdf?sequence=1&isAllowed=y},
}
```

**Reference Type:** Thesis

**Subject Area(s):** Psychology