Population Estimation Through Murder Statistics

For reasons that I no longer remember I found myself looking at the murder rate page on Wikipedia. Looking at some of the patterns in a few of the safer countries I realized that I could estimate their populations based on their homicide rates.

Is that wrong?

Here’s a squished down copy of the bottom of that chart, showing homicides per 100,000 people per year. Can you see the patterns?

image

Monaco

There are only two numbers for Monaco – 0.00 and 3.1. It seems likely that this corresponds to years with no murders and years with one. Therefore that suggests that Monaco has a population of 100,000 / 3.1 = ~32,000

Iceland

Iceland’s numbers generally appear to be multiples of 0.34 to 0.35, with the recent numbers being 0.31. That suggests that the years with a murder rate of 0.31 and 0.35 represent one murder, o.65 represents two, 1.02 and 1.03 represent three, and so on. The declining rate for single-murder years suggests that the population has increased over the years, and is now about 100,000 / 0.31 = ~320,000

Bahrain

Bahrain’s numbers are a bit messier, especially the 0.94 in 2006. However the rest of them appear to be multiples of 0.11. That would give us a population of 100,000 / 0.11 = 910,000.

Morbidly conclusive

How’d we do? On the three countries with small enough populations and low enough murder rates to give us a plausible signal-to-noise ratio, two answers were quite good, and one was mediocre. I didn’t try any others.

Country Estimated population Actual Population Error
Monaco 32,000 35,986 -11%
Iceland 320,000 320,000 0%
Bahrain 910,000 1,234,571 36%

The common divisor for Bahrain, given its population, ‘should’ have been about 0.081, rather than 0.11, but I can’t see that in the numbers. That could indicate dirty data, or a rapidly changing population.

About brucedawson

I'm a programmer, working for Google, focusing on optimization and reliability. Nothing's more fun than making code run 10x faster. Unless it's eliminating large numbers of bugs. I also unicycle. And play (ice) hockey. And juggle.
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4 Responses to Population Estimation Through Murder Statistics

  1. Vlad says:

    Unless I’m missing some very elusive elegancy, I cannot see your logic. Could you please elucidate? And explain why the same logic doesn’t seem to work for any other country?

    • brucedawson says:

      Vlad — Monaco’s murder rate is 3.1/100,000 for three of the years listed. Since the number of murders in a year is always an integer that means that the population must be some multiple of the fraction 100,000/3.1, so it must be about 32,000, 64,000, 96,000, 128,000, etc.

      Given that Monaco’s murder rate is zero for three years and 3.1 for three years, the most plausible explanation is that this corresponds to years with zero and one murders, and therefore a population of 32,000. It could correspond to years with zero and two murders, or zero and three murders, but that seems less likely.

      This technique only works for very low total numbers of murders, and thus for very low populations. The number of yearly murders in the US is over 15,000 so the signal-to-noise ratio prevents this technique from working.

  2. nomnomnom says:

    haha nice

  3. brucedawson says:

    De gustibus non est disputandum. I find it amusing that this article, written and posted on a whim, got picked up by reddit and has been read by more people than some of my meticulously researched and far more useful posts. Not a problem – just interesting.

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