Wikipedia lists the number of billionaires by country. Map 1 shows how these are distributed around the world. Note that billionaires are not all the same, some only have one, others may have many billions of personal wealth, but this is disregarded here. Also, heads of countries are not taken into account regardless of their degree of omnipotence.
In earlier maps I divided the countries in to ten equal sized groups but in this case there were so few values that it didn’t work well. So in this case I made a list of all the different values and divided those to ten about equal sized groups and then populated those groups with the countries that had that number of billionaires. This results in groups that are not equal in size nor do they cover the same portion of the total range, but they do have about the same number of different values in them.
Map 1 tells mostly that there aren’t that many billionaires in Africa, which fits well with my preconceptions. It’s quite obvious that billionaires are at the tail of the wealth distribution. It’s therefore quite natural to think that there are more billionaires if there are a lot of people and/or if the GDP (nominal, the IMF numbers) is high (both Wikipedia links accessed Feb 2013). For GDP I used the nominal one as going for a purchasing power parity correction didn’t seem relevant from a billionaires point of view.
Figure 1 shows the relationship between number of billionaires and the population of a country. Sure enough if there are more people there are more billionaires, but there is also a lot of noise. Figure 2 shows the same for GDP, the linear fit is much better. For completeness’ sake Figure 3 shows the relationship between GDP and population.
Maps 2 through 4 show how the situation changes when size of a country’s population is accounted for, when the GDP is accounted for and when both of the are taken in to account.
Number of billionaires per GDP could be considered to be a rough indication of extremeness of wealth distribution, if for a fairly small GDP there are a lot of billionaires much of the money is in only a few hands. it should also show countries where billionaires go after they have made their fortune.
Number of billionaires per both population and GDP seems a like weird quantity. That is, because GDP times population doesn’t seem to have an obvious explanation. But it could be considered as an indication of political power, as richness and a lot of people both indicate that the country in question likely will be listened to when it has concerns. Number of billionaires per this quantity would then be the inverse of political power per billionaire, which if you think that money equals also political power and not only influence on people is surely something interesting.