Population Utility Distribution

Here we make a first attempt at determining the distribution of utility across today's human population by plotting number of people vs. utility. This plot gives us a snapshot of how today's human population is doing by showing the number of people experiencing a particular utility level. However, the plot provides no information on which people are doing better or worse.

The data for utility is "life satisfaction" data copied from this Happy Planet Index list, which in turn comes from this World Database of Happiness page using this methodology. It features values, on a 1-10 scale, for life satisfaction for most countries, covering about 6.466 billion out of 6.549 billion people alive today. The data was collected during 1995-2005. This data was matched with population data from Wikipedia's List of countries by population.

Unfortunately, the database only provides one life satisfaction value, presumably the average, for each country. To accurately plot the world's utility distribution, we would need the countries' distributions. As a crude compensation, we'll assume that utility follows a normal distribution within each country. I suspect that this is not a reasonable assumption in many countries due to inequities within the population, but for now, it will do. We'll also assume that each country's distribution has the same standard deviation. I was tempted to scale each standard deviation to the corresponding country's Gini coefficient (see list), but the Gini is a measure of income inequality, and given the findings of happiness economics research, I'm reluctant to use income as a proxy for utility within a country. Further study could likely clarify this matter, although for this post's work, having the raw data for each nation would be best.

By forcing the data to normal distributions, there are two variables we can set to any value: The common value for standard deviation (SD) and the increment between successive life satisfaction values. The original data probably had a life satisfaction increment (LSI) of 1, if survey answers were integers (1, 2, ..., 10). The country data used has an LSI of 0.1 (values are of the form 4.3, 7.5, etc.). Here is a series of plots showing three values for SD and LSI:

Here is a larger image of one of these plots:

In the larger image, the two large peaks in the middle are India (left peak) and China. For these countries in particular, having utility/life satisfaction distributions for the population instead of just an average value would be quite helpful.

Here are some questions one could ask about all this and some answers:

(1) How good of a proxy is reported life satisfaction for utility?
This remains an open question. However, in 2006, life satisfaction and happiness are the best we've got. The HPI discussion of life satisfaction provides some argument for life satisfaction over happiness. ("Whilst on the individual level, day-to-day changes in happiness are of interest, at a policy level it is overall satisfaction that gives the best indication of how groups of people are faring.") I have no comment on the life satisfaction vs. happiness debate at this time.

(2) Is it fair to compare these life satisfaction values between different countries despite language and cultural differences?
The paper Hypertension and Happiness across Nations (pdf) by Andrew Oswald and David Blanchflower suggests that it is. The World Database of Happiness methodology page has more.

(3) What about life expectancy?
HPI uses life expectancy in its statistic, because it's "often regarded as a gold-standard measure of well-being". HPI's combined well-being statistic is life satisfaction times life expectancy. I disagree with using life expectancy in this way because well-being should be more accurately built into life satisfaction. However, assuming individuals' lifetime utility curves resemble Figure 1 of the post Utility Curves and assuming the life satisfaction surveys were not given to a random sampling of people independent of age (in particular because individuals below a certain age are incapable of responding to the survey), then averages should be adjusted accordingly. Using these assumptions, countries with longer life expectancies will have higher average life satisfaction values because their residents will spend a larger portion of their lives during ages in which high life satisfaction is experienced.

Here is the MatLab code I used: life_sat_dist.m. It requires this text file: sat_pop.txt. I merged the data using the Excel spreadsheet file: WorldData.xls. The spreadsheet file also contains the "6.466 billion out of 6.549 billion people alive today" calculation. You may use any of these files for any purpose.