People can come up with statistics to prove anything; 14% of people know that. – Homer Simpson.
Statistics are a useful, sometimes even necessary, tool for thinking about social policy. They help us to check out own limited experience, intuition, and reasoning against a broader field of evidence. At the same time, statistics are often misleading and can be manipulated to make people draw false inferences from a statistic that aren’t warranted by the evidence.
Take, for example, the death penalty. There is a claim bouncing around the internet that 94% of executions are carried out in China, Iran, Saudi Arabia and the United States. The claim is a little out of date, but is technically true. In 2005, 94% of executions were carried out in China, Iran, Saudi Arabia and the United States. It’s equally true that in 2005 91% of executions were carried out in China, Iran, Saudi Arabia and France. That’s because in 2005 91% of executions were carried out in China, Iran, and Saudi Arabia. Told that a high percentage of x happens in countries a, b, c, and d, many people will assume that the percentage of x in country d must be fairly high as well. But this is a faulty inference. For all the statistic tells us, the percentage of x in country d could be zero (as it is in the case of executions China, Iran, Saudi Arabia, and France).
Ultimately, of course, looking to a country’s percentage of executions as a way of determining whether that country carries out the death penalty too often doesn’t make much sense. If China were to abolish the death penalty tomorrow, the U.S.’s share of executions would shoot way up, not because the total number of executions in the U.S. would go up, but because the total worldwide had fallen. Likewise, if other countries were to radically expand their use of the death penalty the U.S.’s share of executions would fall, but this wouldn’t mean that we were executing fewer people. What matters is not whether a given instance of capital punishment raises a countries share of executions above a certain percentage; what matters is whether that given instance of capital punishment is just.