Averages, Percentages and Moral Equivalence

From Asturias.

Not long ago I praised Steven Pinker’s Better Angels of our Nature for its clarity and as one of the sources for how I frame my general sense of optimism. At the same time, I repressed a feeling of uneasiness stemmed by the numbers that were put forward.

There was, indeed, something strange lurking in the numbers. Initially I attributed it to my reactions to his harsh words on tribal and indigenous cultures, assigning higher rates of violent conflict versus our civilisational environments, which suffer from more existential forms of violence. I also thought it was merely because he sided with Hobbes in the Hobbes/Rousseau debate, and being on Rousseau’s side in this dichotomy, it also disturbed me.

But cases for all these criticisms have been voiced enough. Instead, I became interested in the metrics themselves. In social sciences, the trend towards quantitative and mathematical formulations has always interested me, first as an active participant, then as a sceptic. More concretely, the way mathematical language has infiltrated thought as a purveyor of truth. If calculations are correct and someone else can verify them, then the theory where math was used must be somehow true by osmosis.

This becomes particularly glaring when the variables and metrics used are squishy and ambiguous. While the measurement of weight or charge for example (despite their relative values to an arbitrary collectively decided measuring stick) entail numbers that include little room for doubt as to where they mean anything and can therefore be fed to mathematical formulas and output meaningful numbers, the variables used to measure anything relating to human activity are much more contentious and it is hard to say what basic algebra means when variables contain lives, concepts and cultural phenomena.

Some of these calculations are used extensively in Pinker’s book. He does a good job of shielding himself from naive mathematical analysis with murky data by selecting the closest to a physical measurement possible: murders, assaults, as reported and recorded by authorities. While there’s a whole lot to say about that, this is not what I’m looking into. Instead, let’s accept the idea that the total number of murders per capita, for example, is a good metric. It’s indeed fair to say we can tell a dead person from a living person, and with some degree of confidence whether a death was a murder. Consider now, this hypothetical data set from two groups of human beings:

GroupTotal PopulationViolent MurdersRate of violent murders (%)
A1002020%
B1000404 %

There are two types of numbers in this table. One type is a measurable quantity, population or number of violent murders are natural numbers—one murder means one individual died. It is not clear at all what half one would be. But for me, the interesting number here is the rate per capita, which was used extensively in Pinker’s book. In my example, the total number of violent murders doubled, but the murder rate was one fifth. Depending on the point we are trying to make, one might say ‘the murders doubled in group B!’ while others might say ‘the murders per capita declined tremendously in group B.’

This is just numbers being instrumentalised to prove a point. Not something new at all. Instead, I’m interested in another, slightly less intuitive property of using ratios as a comparison.

First, using a ratio is perfectly fine for ballpark estimates and thinking clearly, but it is important to understand that a ratio is always meaningless without at least one of the values used. If I say murder rate is 5%, that number can mean 5 people (100 people in a group) or it can mean 5000 (100000 people in a group.)

In both cases the ratio is the same: 5%. The totals, however, are drastically different. When we compare ratios without using the base values we used, we lose the sense of scale, i.e., 5 people dead or 5000 dead become morally equivalent if our comparisons are done exclusively in terms of ratios.

Looking again at the first example, by saying there was moral progress from group A to group B due to a 5 fold decrease in murder rates we are, implicitly, creating a moral equivalence between 20 dead in group A and 40 dead in group B. Each dead person in group B is effectively worth less than one in group A. If we consider each one of those individuals lived a full life and their death was an immeasurable and indivisible tragedy, we realise immediately that I could kill someone in group B and they would only count as half a person in group A. To what extent can we create these equivalences? I tend to think it’s tricky business to say a 4% death rate is better than a 20% death rate if the absolute values are so drastically different.

This implied moral equivalence is what disturbed me about these calculations. 2 dead in group B are 1 dead in group A. The metric doesn’t reveal the true scale of crime, only the relative scale of crime, which for me creates a problematic situation where to increase the number of murders without increasing the murder rate one only needs to increase the population. If what we look at are ratios per capita, we can effectively kill more people while making the murder ratio go down. This is what I concluded was the driving factor for my uneasiness with the book.

This idea that mathematical calculations in social and political sciences create moral equivalences is not new. There’s one big elephant in the room when it comes to creating moral equivalences based on numbers—money. While we frequently might discuss this in the political sciences, it is not uncommon that the use of mathematical language creates its own problems and ends up creating moral equivalence problems like money does.

To discuss rates is to implicitly create an equivalence between the quantities in numerators and denominators, between 5 dead and 50 dead, 50 dead and 500 dead. Since rates alone don’t carry scale, it is simply too easy to simplify and accidentally legitimise big crimes because their relative weight has decreased. I have a hard time saying 50 dead are the same as 5 dead, and reading it as a main thesis disturbs me a great deal.

Speaking of people, societies or collectives in quantities and averages using the mathematics we have today reflects little more than a need to add some mathematical weight to an otherwise subjective theory. Thing is, as we say in computer science, garbage in, garbage out. No matter how good your calculations are, if your starting metrics are subjective, then mathematics is little more than a masturbatory exercise to wow those that have less mathematical knowledge. A bit like illusionism, flashing a nice equation is like misdirection—it allows the theorist to get away with points that would otherwise not survive scrutiny.