Do you know that even if you are 99% accurate in judging a person to be a certain kind of sinner that, if only one percent of the population has that particular sin, you will be wrong in about half your conclusions?
We live in an age of “judgmentalism”. Day by day the media invite us to establish the guilt of others through gory details of high and low crimes. Obviously we are surrounded by big-time Sin. But our focus on the sins of others seems more and more skewed toward the abnormal and the exotic. Weird sin is all the rage these days.
In this article I need to lay a little mathematics on you. The math is not difficult and I have a good reason: it turns out that a statistical theorem of the Reverend Thomas Bayes (1702-1761) can show us how our thinking about modern social issues can go astray.
News headlines as I am writing state that several rock-stars have been arrested on child pornography offences. A particularly disturbing crime, child abuse is much in the news. Jesus himself said that it would be better to drown with a millstone around the neck than to abuse a child (Mark 9:42, Luke 17:2). Obviously child-abusers must be denounced and restrained. However appropriate action rests on our ability to judge accurately.
If we make a mental list of sinners, what percent error can we expect on our list? This is the type of question Bayes’ theorem guides us to answer.
First, obviously the answer depends on the accuracy of our judgment. Not so obviously, it also depends on the frequency of particular sins in the population. Let’s say we are 99% accurate in judging someone to be a sex-criminal when that person really is a sex-criminal. Let’s also say we are 99% accurate in judging a person not to be a sex-criminal when in fact the person is not. Let us also say (to make things simple) that one person out of a hundred is a sex-criminal. What percentage of error can we expect on our mental list of sex-criminals?
If you said 1% error (99% accuracy) you would not be alone. Most people, most of the time, give such an answer – unless suspecting a trick question. However, you are quite wrong. The true answer is somewhere near fifty-percent error!
However, among the ninety-nine (nearly 100) people who remain on our list, we are also likely to judge one to be a sex criminal. Why? Because we are wrong one percent of the time in judging people to be sex criminals when actually they are not.
Because we have misjudged one of the remaining ninety-nine non-sex criminals, we have a total of two on our list when only one really fits the bill. One right and one wrong give us 50% error.
Our mental list would be 99% accurate only if the frequency of sex criminals in the population were 50%.
Time and again, governments and private organisations have tried to set up “registries” of such criminals as child-abusers. Even when based on indictments and convictions, these always contain a far higher percentage of “errors of co-mission” (people misjudged to be guilty) than was intended or expected (Central Registry: Protection or Oppression). It seems government bureaus as well as individuals are strongly disposed to overestimate the accuracy of their judgments. Such registries are very expensive to maintain and must be continually revised and defended against complaints and litigation.
It is something to think about, isn’t it? The solution, of course, is to trust God and not one’s own judgments: that way one can never be wrong.
Or do you get the feeling I’m judging you in writing this?
Thomas Bayes, by the way, was a “Nonconformist” Minister who, in the late 1720’s became minister of the Presbyterian Chapel in Tunbridge Wells, southeast of London. Although Bayes was recognised as an excellent mathematician, his esteemed theorem was not published until after his death.