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 per cent of the population has that particular sin, you will be wrong in about half your conclusions?
We live in an age of “judgementalism”. 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 difficult but I have a good reason: it turns out that a statistical theorem http://en.wikipedia.org/wiki/Bayes’_theorem of the Reverend Thomas Bayes (1702-1761) can show us how our thinking about modern social issues can go astray.
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. And Jesus also warned us not to judge lest we be judged (Luke 6:37, Matthew 7:1)
If we make a mental list of sinners, what per cent error can we expect on our list? This is the type of question Bayes’ theorem guides us to answer. http://www.bayesian.org/ Even if you have trouble (as I do) remembering and understanding the mathematical formulae, you can still grasp the principle:
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-per cent error! Here’s why:
Let’s say we judge a hundred people. Among them, we can expect one to be a sex criminal and, since we are right 99% of the time, that one will be on our list and rightly so. 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 per cent 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. http://www.ipt-forensics.com/journal/volume3/j3_4_6.htm. It seems government bureaus as well as individuals are strongly disposed to overestimate the accuracy of their judgements. 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 judgements: 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 1720s became minister of the Presbyterian Chapel in Tunbridge Wells, south-east of London. Although Bayes was recognised as an excellent mathematician, his esteemed theorem was not published until after his death. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Bayes.html