James Jimenez on Benford Law

A Pro Pinoy member saw this on Comelec spokesperson James Jimenez’ Facebook. The team decided to repost it here.

Benford, shmenford
James Jimenez

I wish Dr. Felix Muga – an old friend from when I used to comment on Filipino Voices – could have explained Benford’s Law better to reporters. You see, ABS-CBN’s Ryan Chua quoted him.

Dr. Felix Muga, a mathematics professor at the Ateneo de Manila, cites Benford’s law in statistics, which states that “in lists of numbers from many (but not all) real-life sources of data… the first digit 1 is almost one third of the time, and larger digits occur as the leading digit with lower and lower frequency…”

Thus, if a candidate is associated with the numeral 1 or is first on the list, he or she has 30 percent more chances of “occurring” or being chosen than others. Those close to his or her name have good but lesser chances.

“The effect is usually on the undecided voters. Their tendency is to go to the number one on the list first,” Muga says.

Now, just from that snippet, it’s pretty hard to say whether it was the good Dr.Muga who gave the explanation or Mr. Chua, but it’s a deadringer for a wikipedia entry:

Benford’s law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 almost one third of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than one time in twenty.

The only difference being that the first quote didn’t make sense (an editorial oversight, probably), while the second one was clear as crystal.

According to the Wikipedia, Benford’s law simply states that in many lists of numbers most of the first digits will be a one (1). Two’s are less common, three’s are even rarer, and nine’s are the least common of all. You get it, right?

Okay. So,where does it say that “Thus, if a candidate is associated with the numeral 1 or is first on the list, he or she has 30 percent more chances of “occurring” or being chosen than others. Those close to his or her name have good but lesser chances.”

That word “thus” in that quote is so misplaced because Benford’s rule apparently doesn’t support the conclusion being forcibly drawn from it. Writing a multi-digit number that starts with the number one is such a far cry from “picking the first on the list” that it boggles the mind how such a connection could even be made. That’s like a textbook non sequitur, baby. It simply does not follow.

In fact, it CANNOT follow.

The closest that Benford’s law has so far come to elections is when it was used to “hint” at possible fraud in the Iranian elections recently.

To dig deeper, Boudewijn Roukema of Nicolaus Copernicus University in Torun, Poland, used a mathematical tool called Benford’s law. In many random sets of data, numbers are more likely to begin with 1 than any other digit. The next most frequent starting digit is 2, then 3 and so on, in a precise relationship. The law applies to any set of numbers scattered randomly on a logarithmic scale.

Any deviation from this pattern could suggest that figures have been manipulated. This has been used to uncover tax fraud and false expenses claims, and Roukema now says it points to fraud in the Iranian election. He analysed the vote counts reported for the four candidates in 366 districts. Votes for three of the candidates fit expected patterns, but Karroubi has an unexpectedly large number of counts beginning with the digit 7. The chance of such a large deviation from Benford’s law happening without foul play is only 0.7 per cent, Roukema says. “The simplest interpretation would be that someone interfered in the overall counts per district.”

So, to simplify: Benford’s law does not speak of the choices people make – in particular, selecting the first name on a list – rather it speaks of how numbers randomly appear on huuuuuge lists. In fact, it is precisely when human choices are introduced – as when cheaters make up fictional election results – that Benford’s law breaks down. That breakdown then becomes the indicator of fraud.

So it’s kinda irresponsible to be invoking Benford’s law to say that your candidate is disadvantaged because he isn’t number one on the list. Benford has NOTHING TO DO WITH THAT.

If I had a dirty mind, I would be so tempted to say that invoking Benford’s law is meant to take advantage of the average joe’s ignorance; meant to bludgeon him into submission with the use of magic words that he won’t understand anyway so he’ll just have to rely on the credentials of the person making the announcement – ‘after all, he did say it was based on a law of statistics, uh-huh, yessuh! Not just a theory, mind yuh, but a gosh-darned full-fledged law!’

But then I don’t have a dirty mind, so I’ll just go see how those Acosta cups are doing over at 7-11.

Karen Ang

A plebeian who is trying to make small changes in this world.