Q&A: The Representativeness Fallacy
The Representativeness Fallacy
Question
Rabbi Michi, hello,
I read your article on the above topic several times (the one published in Assia), and there’s something I didn’t understand that really bothers me. At the beginning of the article you write:
To what extent does the prevalence have to be high for the test to be reasonably reliable? The measure is the ratio between the reliability of the test and the prevalence of the disease. If they are of the same order of magnitude, then the results begin to become meaningful.
But in the last part, where you try to apply this to the Talmudic passage about virgins and non-virgins, you say the exact opposite:
Now one can see that this test is not successful, because the prevalence of the phenomenon it is meant to examine is similar to the reliability of the test. If indeed the voice were present in a large majority of women married as virgins, meaning the test were much more reliable, then one could rely on it even to examine a phenomenon that is not so common. Everything depends on the ratio between the majorities (the reliability of the test versus the prevalence of the phenomenon).
I would appreciate a clarification.
Answer
I no longer remember the details, but it depends on what kind of conclusion you’re looking for. If you want a clear-cut determination, then the holes in the testing net need to be much smaller than the fish. But if you just want there to be a meaningful doubt, it is enough that they be about the same size. After all, if the holes are the same size, you’re talking about something like 50%. That is not enough for a determination, but it certainly is enough to create a meaningful doubt.