The importance of being "one" (or Benford's law)

Corazza, Marco; Ellero, Andrea; Zorzi, Alberto

doi:10.1007/s40329-018-0218-4

In this article we give an informal presentation of the so-called Benford's law, a counterintuitive probability distribution that describes the frequency with which the first significant digits - that is, a digit between 1 and 9 - appear in sets of numbers associated with heterogeneous quantities. Unlike what might be expected, these frequencies are not equal but are decreasing, that is, 1 appears more often than 2, which appears more often than 3 and so on. After an introduction to the law, we will show how, perhaps unexpectedly, it is satisfied by the numbers generated by some sequences of powers. We will then illustrate some applications in the socio-economic field (for instance, to identify accounting or electoral fraud). Finally we will use it to analyse the tax returns of some former US presidential candidates.

In this article we give an informal presentation of the so-called Benford’s law, a counterintuitive probability distribution that describes the frequency with which the first significant digits—that is, a digit between 1 and 9—appear in sets of numbers associated with heterogeneous quantities. Unlike what might be expected, these frequencies are not equal but are decreasing, that is, 1 appears more often than 2, which appears more often than 3 and so on. After an introduction to the law, we will show how, perhaps unexpectedly, it is satisfied by the numbers generated by some sequences of powers. We will then illustrate some applications in the socio-economic field (for instance, to identify accounting or electoral fraud). Finally, we will use it to analyse the tax returns of some former US presidential candidates.