Generalized Benford’s Law as a Lie Detector

Abstract

The first significant (leftmost nonzero) digit of seemingly random numbers often appears to conform to a logarithmic distribution, with more 1s than 2s, more 2s than 3s, and so forth, a phenomenon known as Benford’s law. When humans try to produce random numbers, they often fail to conform to this distribution. This feature grounds the so-called Benford analysis, aiming at detecting fabricated data. A generalized Benford’s law (GBL), extending the classical Benford’s law, has been defined recently. In two studies, we provide some empirical support for the generalized Benford analysis, broadening the classical Benford analysis. We also conclude that familiarity with the numerical domain involved as well as cognitive effort only have a mild effect on the method’s accuracy and can hardly explain the positive results provided here.

Benford’s law first significant digit and distribution distances for testing the reliability of financial reports in developing countries

“…In fact, such a possibility might not be surprising, or is even sustained, in view of findings on income taxes regularity in some Italian provinces by Mir et al [7,22]. Such an argument suggests to consider alternative methods complementing the BL classical analysis [23,24,25].…”

Abiding by the Law? Using Benford’s Law to Examine the Accuracy of Nonprofit Financial Reports

“…It will also fail to detect fraud when made-up numbers conform to Benford’s Law. Nonetheless, there are only a few studies on this topic and they largely suggest that made-up numbers do not comply with Benford’s Law (Burns, 2009; Gauvrit, Houillon & Delahaye, 2017). 2…”

Benford's Law as an Indicator of Survey Reliability—can We Trust Our Data?

“…(), for image forensics; and Swanson, Cho and Eltinge (), for consumption expenditures. Additionally, further studies exist that discuss the use of Benford´s law as a lie detector (Gauvrit et al ., ), to detect incorrect information of countries regarding their effort to combat money laundering (Deleanu, ), or to assess the reliability of financial reports in developing countries (Shi et al ., ). The literature thus lacks large‐scale analyses of how individual income data conforms to Benford's law, knowledge that could be used to improve the assessment of survey data quality.…”

“…3 Authors who have used it to evaluate (survey) data quality include Judge and Schechter (2009), mainly for agricultural data; Nigrini and Miller (2007), for hydrological data; Sandron (2002), for population numbers; Mir (2014), for religious data; Ausloos et al (2015), for long-term birth numbers; Fu et al (2007), for image forensics; and Swanson, Cho and Eltinge (2003), for consumption expenditures. Additionally, further studies exist that discuss the use of Benford´s law as a lie detector (Gauvrit et al, 2017), to detect incorrect information of countries regarding their effort to combat money laundering (Deleanu, 2017), or to assess the reliability of financial reports in developing countries (Shi et al, 2018). The literature thus lacks largescale analyses of how individual income data conforms to Benford's law, knowledge that could be used to improve the assessment of survey data quality.…”