Reflections on The Better Angels of Our Nature - part 1

Since its publication in 2011, The Better Angels of Our Nature has been thoroughly reviewed, with the reactions ranging from enthusiastic to snarkily dismissive. The Wikipedia page does a good job of summarizing the argument and its reception, so there is not much left to add, apart from some personal impressions:

Almost absent from the reviews¹ (although, in my opinion, it is one of the main merits of the book) is the central role played by Norbert Elias and his Civilizing Process.This process is one of the explanations put forward for the spectacular decrease in violence.

The other cause Pinker invokes for the reduction in violence since the Middle Ages (in Europe, at least) is what he calls Enlightenment humanism, or classical liberalism (at the end of Chapter 4). This tradition is not easily defined, as one can see from John Gray's objections that the authors cited by Pinker “are highly disparate thinkers, and it is far from clear that any coherent philosophy could have 'coalesced' from their often incompatible ideas”² and that some of them, such as the French revolutionaries, advocated the use of violence. However:

• The historical evolution of an idea cannot involve homogeneous thinkers (otherwise there would be no evolution). Of course Hobbes and Mill have different positions, but nobody would deny their contribution to liberalism.
• Pinker rejects the idea that the Enlightenment is responsible for the French Revolution and its bloody aftermath (including Napoleon). To prove him wrong, one should at least engage his argument.
• The intellectual contribution of an author is more important than his having held acceptable morals. For instance, some consider Machiavelli a precursor of liberalism.

The very substantial chapter 5 "The Long Peace" discusses whether the reduction in violence since the end of World War II is a systematic effect. The weakest link here is estimating the effects of ancient conflicts, such as the An Lushan revolt in 8th century China, which purportedly killed 36 million people in eight years. This figure corresponds to the difference in census data before and after the rebellion, but the reduction could also be due to loss of territory, refugees, weakening of the administration (leading to less reliable information) etc. On the technical side, Pinker gives an interesting argument that the magnitude of attrition wars is exponentially distributed, but introducing an escalation component can turn the distribution into a power law. I gave the detailed derivation of this result in a previous post.

(to be continued...)

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^{1. Notable exceptions are Peter Singer and James Q. Wilson. ↩}

^{2. In the next phrase, Gray takes Pinker to task for not adding Marx, Bakunin and Lenin to the list. Apart from the intrinsic incoherence of this argument, the point is addressed three pages later, where Pinker explicitly discusses counter-Enlightenment positions, including that of Marx. ↩}

Life expectancy, GDP and HIV prevalence

What explains the variation in life expectancy between different countries? The GDP is of course very important: the LE increases roughly linearly with its logarithm. To remove this dependence I fitted the data with a sigmoidal function:

 \(  LE (GDP) = LE_{\text{min}} + ( LE_{\text{max}} - LE_{\text{min}}) \frac{1}{2} [1+\text{erf} (\alpha \log (\beta \, GDP))] \qquad \qquad (1)\)

shown as solid line in Figure 1.

 

Figure 1: Life expectancy at birth (UN World Population Prospects 2010) versus GDP by country. Overall value (male and female). Color corresponds to the geographical region.

The fit is slightly better than with a simple logarithm and the function (1) makes more sense: the LE cannot increase (or decrease) indefinitely. To give an idea of the dispersion I also plotted (as dashed lines) the same curve but with parameter \( \Delta _{LE} = LE_{\text{max}} - LE_{\text{min}} \) equal to 0.8 and 1.2 of its optimal value.

In Figure 2 I normalize the LE by the model (after subtracting the baseline) and plot the result as a function of the HIV prevalence. \(y\)-values of 0.8, 1.0 and 1.2 correspond to the lines in Figure 1.

 Figure 2: Life expectancy versus HIV prevalence by country. Color corresponds to the geographical region.

The normalized LE is strongly influenced by the HIV prevalence: All countries below 0.8 in the former are above 1% in the latter, except for Afghanistan (not shown in Figure 2), where the ongoing war might explain the reduced LE.

How can one understand the few LE values above 1.2?

Death by firearm, gun possession and the GINI coefficient

The recent tragic events in Newtown rekindled the debate on gun control and the interest in the correlation between gun ownership and gun-related deaths. The issue is clearly very complicated, and a single variable will not explain much, but it would still be interesting to plot the interdependence of the various parameters. Of course, I claim no causality relation between them.

The most obvious variable couple to plot is the number of gun-related deaths vs. the number of guns per capita (both retrieved from Wikipedia). When I was halfway through the data treatment I noticed that a similar graph was made by Mark Reid. The plot is below, in log-log representation, since both the x and y axes cover more than two decades:

The three-letter country code is retrieved from here. The data seems to follow a linear tendency (dashed line), but even in a log-log plot some deviations are clearly visible, such as the cluster of values at top center (dashed frame).

I decided to consider some additional (economical) parameters, and the results are quite interesting.  Another variable that could be correlated with gun violence is the economical inequality, quantified for instance by the GINI index. Plotting the number of firearm casualties versus this variable (I used the coefficient defined by the World Bank, fourth column in the table) yields the following graph:

The "anomalous" points in the first graph now follow more or less the same tendency as the other countries (the dashed line is a guide for the eyes). The gun ownership is used as color code (see the legend), but values between 2 and 20 are difficult to distinguish in this log scale. A nice feature is that the countries with low gun ownership (in blue) which were at the bottom left in the first graph also follow the tendency in the second one.

Visually, I would say that the GINI coefficient explains the data better than gun possession. What other variables might be correlated with gun-related deaths ? For instance, below is the GDP dependence (data from here):

For the USA, the relation between firearm deaths and gun ownership can be seen, for instance, here. How about the economical indicators ? I retrieved GINI values for the US states in 2010 and the number of firearm murders in 2011.

[29/03/2018: I had used the wrong data for the graphs, as pointed out by an anonymous comment (see below). This is now corrected, but the general conclusions still hold.]

The graph is below, in lin-log representation:

The GINI range (41-50) is much smaller than the global scale (12-65 percentage points) but there is a clear correlation. This may not be all that surprising, since firearm murders are extremely well correlated with the total number of murders (and the correlation between inequality and violence seems intuitively plausible). What I find more interesting is that there is almost no dependence on the GDP per capita:

In both graphs I left out DC, which is far to the right of the other points in both inequality (53.2)  and GDP (174500) with a y value of 77, as well as HI, which has a very low murder rate.

It would therefore seem that the inequality is strongly correlated to firearm casualties, both for the US states and for world nations.