Emotional reactions to numbers

Inability to be random can help detect fraud

By Daniel Packard, CFE, CPA

Investigate This: Interviewing, data analysis, digital forensics and more

This new column explores facets of the investigation component of fraud examinations. — ed.


When I was in college, one of my professors — while teaching the composition of random sequences — asked the students to randomly arrange themselves throughout the classroom. A birdseye photo from the ceiling was then taken of the distribution. The results were shocking. A true random distribution would have clusters and outliers, but we were equidistant from one another.

My professor explained that humans can't create true random sequences. The ability to create randomness seems fundamental to cognition because it involves noticing structure, or the lack thereof, of events in the world. However, past research has shown that people can't understand randomness and tend to succumb to "over-alternation bias" — the tendency to overdo an alternating sequence in an attempt to appear random.

Years later, my yen for criminal psychology reached its apex late one evening at work. While reviewing a recent "IRS Revenue Procedure," I noticed that my eyes involuntarily perceived the number "1" in a bizarre shade of green, while all other characters were monochromatic. (Stay with me; this isn't as strange as it sounds.)

My initial panic at this phenomenon turned into profound interest as I read about other individuals who've had similar experiences. The condition is generically known as synesthesia — a neurological condition in which stimulation of one sensory or cognitive pathway leads to automatic, involuntary experiences in a second sensory or cognitive pathway. One common form of synesthesia, known as grapheme, deals particularly with the perception of color associated with letters and numbers. My mind had developed an involuntary, subconscious response to the number "1."

These experiences suggested to me the following:

  • Our minds have a natural, predictable proclivity toward certain patterns and symmetries.
  • Our minds have the capacity to involuntarily evoke secondary responses to otherwise unrelated stimulations.
  • We can generalize and exploit these tendencies in the detection of fraud.


As illustrated in the ACFE's 2012 Report to the Nations , researchers — and fraud examiners — have thoroughly analyzed fraudsters for their proclivities to commit fraudulent acts. Quantitative observations of a perpetrator's position, gender, age, tenure, education level and employment history help determine an individual's motivation, opportunity and rationalization to commit fraud. The report also illustrates perpetrators' qualitative red-flag behavior regardless of these same factors.

Perpetrators continually display psychological behavioral traits consistent with the stress or fear of committing fraud, including living beyond one's means, having an unusually close association with vendors or customers, irritability, suspiciousness, defensiveness, complaining, addictive problems and excessive control issues. While fraudsters' circumstances may vary, all are subject to the psychological behavior traits inherent to perpetrating fraud.

The pervasiveness of these psychological behaviors is strongly correlated with the most common source of detection — employee tips. According to the report, employees' ability to discern these red-flag behaviors among peers accounts for the most effective method of detection. This suggests to me that of all the sophisticated tools used to detect fraud, a fraud examiner's most powerful and effective instrument is the ability to emotionally and psychologically profile the perpetrator. Furthermore, we could potentially generalize and exploit other subconscious responses associated with the stress and fear of perpetrating fraud in the computational detection of fraud.

Can we exploit humans' inability to generate a random sequence in detecting fraud? Scientists through the ages have substantiated claims of predictable, evenly distributed and symmetrical tendencies in humans. We've expressed this symmetrical preference in geometry, science, history, religion, musical theory, architecture and worldwide culture. While some of these observations may be too abstract to conclusively infer an individual's inclination toward a numerical preference, it's useful in illustrating that several aspects of our lives seem to suggest a symmetrical, evenly distributed preference. Furthermore, these external forces can often have an involuntary influence on otherwise unrelated aspects of one's life.

Perhaps the most persuasive research about perceived randomness is Ruma Falk and Clifford Konold's claim that people associate the randomness of a sequence with difficulties in "mentally encoding." (See "Making Sense of Randomness: Implicit Encoding as a Basis for Judgment," by Falk and Konold, Psychological Review, 1997, Vol. 104, No. 2, 301-318.)

We optimize perceived randomness when we maximize "cognitive complexity." The perceived difficulty of a sequence is primarily rooted in our ability to add, subtract, multiply or divide certain numbers. Consequently, we perceive prime and odd numbers as cognitively complex and difficult to encode when compared to their even-numbered counterparts. To some general extent, the Western world has collectively developed a synesthetic secondary response to odd and prime numbers. While we may not perceive these numbers in shades and hues, we may involuntarily assign unique emotional reactions to certain numbers. Perhaps we've involuntarily categorized these numbers as evasive, deceptive, complex and ambiguous.

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