Quantifying Violence



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Suppose there are two countries, comparable in all aspects of quality of life, except in one of them there are 13,400 intentional homicides every year, and in the other the number is 56. Which one would you prefer to live in, if you had the choice?

The reason I am asking this question is that I am currently working my way through Steven Pinker’s The Better Angels of Our Nature: Why Violence Has Declined. My intent is to write a critique of his book from the point of view of Cultural Evolution. Surprisingly, as best as I could determine, this hasn’t been done. My critique, however, is going to focus on his explanation of why violence has declined, not on whether it’s happened or not.

Pinker’s book has sparked quite a controversy, but the main thrust of his critics has been on the empirical trends. Did violence really decline? I have discussed some of it in previous posts, in particular the one where I reviewed the recent article by Azar Gat.

But in this post I want to ask an even more basic question. In order to answer the question of whether violence has declined, we need to measure it. Pinker has followed the standard approach in criminology by focusing on the rate of homicide; that is, the number of people killed per 100,000 population per year. It seems the logical way of doing it; which is why I was surprised to see that many of Pinker critics chose to attack him by saying that rates are misleading—we should look at the absolute numbers.

For example, in a review in Scientific American, Robert Epstein wrote:

Of greater concern is the assumption on which Pinker’s entire case rests: that we look at relative numbers instead of absolute numbers in assessing human violence. But why should we be content with only a relative decrease? By this logic, when we reach a world population of nine billion in 2050, Pinker will conceivably be satisfied if a mere two million people are killed in war that year.

It seems to me that only a deeply innumerate person could write this (innumeracy is mathematical illiteracy; incompetence with numbers rather than words).

Since a respected publication, Scientific American, published such a critique, perhaps the point is not as blindingly obvious as it seems to me. So here’s how I would explain it.

Let’s think about homicide as a component of quality of life (a negative one to be sure). In fact, because the right to life is the most basic human right, surely reducing the probability of being deprived of it by intentional homicide should be on the top of our agenda. But the probability of being killed is directly related to the homicide rate, not to the absolute number of homicides. A homicide rate of 50 per 100,000 means that you have a 0.05% chance of being killed in any particular year. This may not sound like a lot, but over a life span of 70 years it accumulates to a whopping 3.5 percent. In Honduras, where the murder rate is close to 100 per 100,000, and life expectancy is 73.5 years, the chances of ending your life by being murdered accumulate to more than 7 percent. Since males are much more likely to be murdered than women, their chance is at least double that. Let’s say it’s 16 percent, or one in six (probably an underestimate). What this means is that every male born in Honduras is automatically enrolled in a game of Russian roulette with a six-gun.

And now back to the question I asked at the beginning. 56 homicides per year is how many people are killed in the U.S. Virgin Islands. The homicide rate there is a 50 per 100,000. According to Wikitravel,

Some parts of St. Thomas, especially Charlotte Amalie can be very risky at night. Drugs and other related crime are a major problem, and dangerous public shootouts are a fact of life around St. Thomas. Tourists should exercise extreme caution when getting around as some neighborhoods can be dangerous, even if a well-known restaurant is in a particular neighborhood.


US Virgin islands the most underrated place in America?

13,400 homicides is the number for China. But because China has much larger population than U.S. Virgin Islands, the homicide rate in China is only 1 in 100,000. All travelers in China comment on how safe they felt there.

Now I agree that St. Thomas has wonderful beaches, and China, not to put too fine a point on it, is a dictatorship. But there are plenty democratic countries with fine beaches, so let’s focus on the question of personal security. If you had a choice of moving to a country in which you would be 50 times more likely to be murdered, compared to the alternative, would you do it? Most of us, who don’t have a death wish, surely would choose a country with a lower homicide rate, no matter what the absolute numbers are.

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That is a rather strange criticism, and the review as a whole is fairly weak. Another fallacy it engages in is equivocating between trends and levels. Pinker’s argument is that the rate of violence has declined, and presumably this statistic is correct (actually, it is in fact correct). The fact that wars and armed conflicts still happen, as Epstein notes in the opening paragraph, does not in any way invalidate the thesis.

I agree then that pretty much for all practical purposes it’s the rates that one should be looking at not, not absolute numbers. These practical purposes involve both understanding violence, and also devising policies and institutions which reduce it. Epstein’s criticism is a bit like when people compare countries.by their total GDP rather than GDP per capita.

Actually, that’s not quite the right analogy. It’s more like comparing countries by the total number of people in poverty rather than the poverty rate. If we have one world with 100 people and 2 poor people, and another world with 10000 people of whom 100 are poor one could argue that there is more total misery in the second one, even though the rate is lower, hence it’s a worse world. Maybe.

So if I was going to make an argument for attaching importance to absolute numbers and not just rates, I’d say there’s a sort of “repugnant conclusion in reverse” at issue here (after Parfit); adding enough additional people can compensate for lower average happiness. In moral theory this often comes up, especially when doing some kind of utilitarianism. The “maybe” above refers to the result that if one rejects the kind of logic that leads to the repugnant conclusion, then pretty much one must reject the possibility of comparisons among societies of different population size, which isn’t very satisfactory.

Jay Ulfelder

As a classical liberal, I agree with you that the rate and not the count is the more relevant number.

One small statistical quibble, though. To determine the cumulative probability of death by homicide by a certain age, we can’t simply sum annual probabilities over years lived, because those probabilities across years are not independent; instead, there is some chance that the individual will have been removed from the risk pool by homicide in a previous year. Put another way, the probability of death by homicide at age x is conditional on survival to age x, and the summing has to account for that. I think I’ve got it right here:

p(death by homicide by age i) = (1 – rate)^age[i] * (rate * age[i])

For age 70 and a homicide rate of 50 per 100,000, that formula gives us a cumulative probability of death by homicide of 0.0338 instead of 0.035.

Jay Ulfelder

Whoops, got the math wrong in that last comment. I think it’s actually:

p(death by homicide by age i) = 1 – [(1 – rate)^age]

That gives us 0.0344 for age 70.

Michael Finfer, MD

“Since males are much more likely to be murdered than women, their chance is at least double that. Let’s say it’s 16 percent, or one in six (probably an underestimate).”

Let’s put some perspective on that. An ordinary woman with no risk factors has about a one in nine chance (11,1%) chance of developing breast cancer in her lifetime. A 16 percent chance of being a homicide victim is only about 44% more than that. Personally, I think that is a huge risk. If the incidence of breast cancer suddenly increased by 44%, the public health authorities would be all over it. Even at current rates, we spend lots of resources screening women for breast cancer.

At 50/100,000, the lifetime risk of being a homicide victim is about 1/3 of that ordinary woman’s risk of breast cancer. I still think that is very significant.

Ross Hartshorn

I am reminded of Nassim Nicholas Taleb’s vehement denunciantion of Pinker’s book (which I read and liked). I like Taleb, but it is clear that he is not able to think calmly or rationally about the thesis that violence has declined. Perhaps, it is related to the fact that he grew up in Lebanon at a time when it was falling apart into civil war. That has to make it hard to think calmly and rationally about war.

I think something similar happens to a lot of people when they think about war and violence generally. They react with such negative emotion to the topic that anything which sounds like “It’s not so bad, you know, it’s been getting better for a long time now”, that they can’t think straight.

Ross Hartshorn

That’s a good point. Pinker’s book is written from the long point of view, and that isn’t a typical POV.

Also, we have a news distribution system which emphasizes the unusual, so that (for example) police officers killing people are reported more than cigarettes killing people, even though the latter may be taking more lives. I think that makes it difficult for people to process the fact that homicide rates are in a long-term decline.

I like Pinker’s book but I’m not sure I buy his proposed reasons for the decline.

Yoram Gat

I have not read the book, but if all the evidence cited is about decline in murder rates then that should also be the subtitle of the book: “why murder rates have declined”. Violence is a much more complex phenomenon than murder rates.

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