“Street-fighting Maths” and Nigeria vs Exxon

I just came across a book with the promising title „Street-Fighting Mathematics — The Art of Educated Guessing and Opportunistic Problem Solving“ by Sanjoy Mahajan (2010), which is actually licensed under Creative Commons, so it can be found for free online. The basic premise is to provide some mathematical tools or heuristics to sufficiently approximate solutions to everyday problems (and maybe also provide a more general framework for that kind of reasoning). And it starts teasingly with a topic called „Dimensions“ and „The power of multinational corporations“. Here’s the problem:

In Nigeria, a relatively economically strong country, the GDP [gross domestic product] is $99 billion. The net worth of Exxon is $119 billion. “When multinationals have a net worth higher than the GDP of the country in which they operate, what kind of power relationship are we talking about?” asks Laura Morosini.

What is the most egregious fault in the comparison between Exxon and Nigeria?

The compelling solution:

The mistake lies in comparing incomparable quantities. Net worth is an amount: It has dimensions of money and is typically measured in units of dollars. GDP, however, is a flow or rate: It has dimensions of money per time and typical units of dollars per year. (A dimension is general and independent of the system of measurement, whereas the unit is how that dimension is measured in a particular system.) Comparing net worth to GDP compares a monetary amount to a monetary flow. Because their dimensions differ, the comparison is a category mistake and is therefore guaranteed to generate nonsense.

So where does this leave one of the central tenets of the anti-globalization movement?

I often see comparisons of corporate and national power similar to our Nigeria–Exxon example. I once wrote to one author explaining that I sympathized with his conclusion but that his argument contained a fatal dimensional mistake. He replied that I had made an interesting point but that the numerical comparison showing the country’s weakness was stronger as he had written it, so he was leaving it unchanged!

A dimensionally valid comparison would compare like with like: either Nigeria’s GDP with Exxon’s revenues, or Exxon’s net worth with Nigeria’s net worth. Because net worths of countries are not often tabulated, whereas corporate revenues are widely available, try comparing Exxon’s annual revenues with Nigeria’s GDP. By 2006, Exxon had become Exxon Mobil with annual revenues of roughly $350 billion—almost twice Nigeria’s 2006 GDP of $200 billion. This valid comparison is stronger than the flawed one, so retaining the flawed comparison was not even expedient!

It is only surprising at first glance that Exxons „money flow“ would be a good deal higher than the value of it’s (material and immaterial) assets, and I do think that the comparison is scary and should get us thinking about corporate power.

A lot of the rest of the book is made up of maths that is more likely to come up in the „everyday life“ of an engineer or economist than mine, but I very much appreciate the general approach. I think it is much better to deal with methods that make you conscious of their imperfections than ones that give the illusion of absolute mathematical certainty, especially when the maths itself can at best be based on imperfect numbers.

Datum: Sonntag, 10. April 2011 21:52
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