The fallacy of small percentages

| February 4, 2009

[UPDATED 02/04/09 — 1124 MST]

It appears that Josh Marshall (see below) is just echoing President Obama (maybe that’s what Josh means by “Talking Points Memo”), who said in different interviews yesterday (scroll down to “Little Pork Spending in Bill”) that “most of the programs that have been criticized, as part of this package amount to less than one percent of the overall package.” Of course, if the pork spending is so insignificant and the overall benefit so great, why can’t the Democrats get it through the Senate?


Josh Marshall is complaining over at Talking Points Memo that

The pretty simple fact here is that the Republicans are not willing or able to criticize any of the substantial amounts of spending in this bill. They’re focused on a few tiny parts of it. And too few people are pointing out that these amount to maybe one or two percent of the program total.

In so doing, he is committing (to an extent) the fallacy of small percentages.

Let’s talk first about the fallacy of large numbers, which is best summed up by the 1927 song, “Fifty Million Frenchmen Can’t Be Wrong“. As a freshman at BYU in 1971, I saw tongue-in-cheek signs up around campus stating, “800 million Chinese can’t be wrong! Take Mandarin 101!” (which, by the way, I did, largely because of those signs). But the simple truth is that large numbers do not equal logical proof or support; after all, in the last three US Presidential elections, a total of 170 million votes were cast for the losing candidate.

The fallacy of small percentages takes the opposite tack, that is, it tends to diminish, dismiss or trivialize something solely because it represents a small percentage of the whole. There may be good reasons for dismissing that something on its own merits or because it truly is unimportant, but the fact that it’s a small percentage is not sufficient in and of itself. Here’s a simple response to Josh Marshall: so, then, by your argument, would maybe one or two percent of fecal matter in your drinking water be unimportant or acceptable?

Beyond that, this fallacy is especially in play here because of the massive size of the so-called stimulus package. Once we start talking about a stimulus bill total approaching one trillion dollars, then one billion dollars — surely not insignificant in anyone’s mind — is just 0.1%, that is one-tenth of one percent. And each of those billion-dollar segments, just 1/1000th of the total, represents real taxpayer debt. As I pointed out in a post yesterday, the town of Thornton, Colorado (population 110,000) is scheduled to get $487 million in “stimulus” spending. I have yet to figure out why.

By the way, I don’t disagree with Marshall that the Republicans should be focusing on the large chunks of the stimulus bill as well. But even just “one or two percent” of the stimulus bill represents $10 to $20 billion of unnecesssary spending and real future debt. Almost every guide to personal and business finances makes it clear that the only way to really control your spending and avoid/get out of debt is to focus on the little amounts, because that’s where you really bleed. And when it comes to the stimulus package, even those “little amounts” are pretty massive. As the old saying goes: a billion here, a billion there, and pretty soon you’re talking about real money.

Where is Senator Dirksen when we need him?  ..bruce w..

P.S. The fallacy of small percentages actually comes into play in startup business plans as well, but in the opposite sense. The classic pitfall is to set out the size of the potential market, then say, “If we can get just 5% of that market…”. The fallacy is in assuming that one can readily get “just 5%” or even “just 1%” of the market. This fallacy was a major factor in the bubble of the late 90s/early oughts (remember the pervasive word “eyeballs”?).

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Category: Economics, Main, Stimulus

About the Author ()

Webster is Principal and Founder at Bruce F. Webster & Associates, as well as an Adjunct Professor of Computer Science at Brigham Young University. He works with organizations to help them with troubled or failed information technology (IT) projects. He has also worked in several dozen legal cases as a consultant and as a testifying expert, both in the United States and Japan. He can be reached at, or you can follow him on Twitter as @bfwebster.

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