Jordan, Bayes and Friedman

On seeing this story about Jordan, one's thoughts turn naturally to Bayes' theorem. It shows that the plaggy hootered minger might have been right to take nine pregnancy tests before deciding she was pregnant.
The theorem gives us a way of rationally updating our beliefs in the light of new evidence. In the context of pregnancy tests, it works like this.
First, you multiply your prior probability that you're pregnant by the true positive rate on a pregnancy test.  For the  sake of argument, let's say Jordan thought there was just a 10 per cent chance of her being pregnant, before taking any tests. And let's say the true positive rate is 95 per cent; suppliers claim their kits are 97-99 per cent accurate in laboratory conditions, but I guess the Jordan gaff is not a laboratory. This gives us 0.095.
Then, you multiply  the probability that you are not pregnant (0.9 in this case) by  the false positive rate on pregnancy tests. Let's assume this  rate  is 5 per cent. This gives us  0.9 x  0.05 =  0.045.
Then, you add this number to  our first calculation. That gives  0.095 + 0.045 =  0.14.
Then you divide our first calculation into this number.  This is 0.095 divided by  0.14  =  67.9 per cent.
This is would be Jordan's estimate of her probability of being pregnant, given one test.
This is clearly a low probability. So it would have been entirely sensible to take more tests. Just how many would depend upon the correlation between one test and another; if the test results (or their interpretation) were uncorrelated, a second positive test would raise the probability of being pregnant to 97 per cent. If they were correlated, the probability would be lower.
However, it's easy(ish) to tweak these numbers to justify taking nine tests. Maybe Jordan's prior was less than 10 per cent. Maybe test results were correlated; false results, I believe, are more likely if you're taking some types of medication. Or maybe I'm over-estimating the reliability of the results under the conditions Jordan took them.
So, Jordan might have been behaving as a good Bayesian.
But of course, few of us believe she and Peter sat down and computed Bayes theorem before deciding to do nine tests.
In other words, although she did not behave rationally, she did behave as if she were rational.
And this is where  Milton Friedman  comes in. In his essay, the Methodology of Positive Economics (an excerpt of which is here), he said that economic theories should be judged by their predictive power, not their descriptive accuracy. So, he said, what mattered is that businessmen behave as if they are minimizing a cost function, or that consumers behave as if  they are mazimizing utility, even though no-one actually sits down and solves the equations.
So, isn't Jordan a bit of evidence that the basic postulate of neo-classical economics is valid, in the Friedmanite sense? People might not behave rationally, but even dim ones can behave as if they were rational.

Update: For the benefit of American readers, "plaggy" is a derogatory word for plastic, usually of inferior quality - as in "plaggy gangster", a small-time criminal who thinks he's a big cheese. "Hootered" derives from this fine company. And a minger is a munter or moose. Americans might not possess the phrase "plaggy hootered minger" - though I'm surprised Larry Summers hasn't coined it - but they have the things in abundance. Hope this helps.   

Comments

[Tim Worstallt]

I’m never all that sure about such women being described as dim. Not intellectual, of course, but dim? Taking a reasonable face and two bags of saline and making a fortune doesn’t strike me as all that dim. Then there’s Peter Andre which does rather destroy the thesis.

[Robert Schwartz]

Dialect problem: What is a: "plaggy hootered minger?"

[Tim Worstallt]

At a guess:
Plaggy : Plastic
Hooter: Breasts
Minger: Unattractive woman with overtones of sexual licence.

[Monjo]

If you ever listen to Jordan, she comes across as reasonably sharp. She can cut the mustard at any rate, if not the beef.