About ten years back, I heard Mark Negrini speak at a meeting sponsored by the New York chapter of the Association of Certified Fraud Examiners. He was speaking about the use of Benford’s Law in fraud investigations. He’s brillant, funny, and a great speaker. My very crude understanding of Benford alone has enabled me to make more rapid strides in investigations. In one case, I believe that my explanation of Nigrini’s work led a party, in short order, from categorical denials to helpful, detailed, signed confessions.
Benford’s law (I’m going to let others explain the details) permits the examination of a set of numbers and gauge the probability that the set has been fabricated, or more precisely, that the individual numbers have been fabricated – such as the documentation of false payments, receipts, and disbursements.
Image courtesy of Procsilas Moscas via Wikimedia Commons under Creative Commons license.
Professor Negrini makes software at an obscenely law prices which permits the use of Benford’s law. I’ve never used the software, but his lecture opened me up to new ways of viewing evidence – perhaps best expressed as the idea that, especially when persons or groups may be trying to deceive about point X, sometimes we can find a related factor, Y, and see if this makes things more or less suspicious. It’s a quantitative method which, to use John LeCarre’s phrase, permits us to “try on the facts as if they were clothes and see if they fit.” Very simply – in a “naturally occurring” set of numbers, there will be far more “1s” and “2s” than “7s”, “8s” and “9s.”
RadioLab – a show produced by WNYC, New York’s outstanding public radio station – has done a wonderful show about Numbers (link to entire episode), with a segment called From Benford to Erdös (link to segment).
There was one thread that I thought puzzling – the question of the admissibility of Benford analyses as proof of fraud. In the first instance, I’m not sure that it should be admissible – there are circumstances in which, say a set of expenses which include recurring charge, set by a vendor, at 9.99, might not be an indicator of fraud. Second, it’s hard for me to imagine a circumstance in which a Benford analysis would indicate fraud and wouldn’t, with a thorough investigation, lead to further, less ambiguous evidence of deception. In other words, I think of it as an intelligence-gathering or investigative tool, not a means of proof.
I’ve yet to listen to an episode that didn’t in some respect surprise and amaze me and give me something to think about. What’s entirely predictable – and counterintuitive – is the consistently outstanding quality. (My point is not that they deviate from their own curve – how could they? – but that RadioLab is always worth listening to).
NB: disclosure: I’m a paid member of WNYC, and therefore thave an interest, however attenuated, in enlarging the audience base without my annual contribution having to go up. Further, I’ve got friends on the station staff, but I’ve never to my knowledge laid eyes on Messrs. Abumrad and or Krulwich.
