Wednesday, June 19, 2019

Junia/Junias and the base rate fallacy

I think it would be useful to apply more Bayesian analyses to textual scholarship.

In Romans 16:7, Junia or Junias is described as “famous among the apostles”. Without accent marks (which were not present in the original manuscript) it is not possible to tell purely textually if it’s Junia, a woman, or Junias, a man. Moreover, “among the apostles” can mean “as being an apostle” or “to the apostles”. There seems to be, however, some reason to think that the name Junia is more common than Junias in the early Christian population, and the reading of “among” as implying membership seems more natural, and so the text gets used as support for women’s ordination.

This post is an example of how one might go about analyzing this claim in a Bayesian way. However, since I am not a Biblical scholar, I will work with some made-up numbers. A scholarly contribution would need to replace these with numbers better based in data (and I invite any reader who knows more Biblical scholarship to write such a contribution). Nonetheless, this schematic analysis will suggest that even assuming that there really were female apostles, it is more likely than not that Junia/s is one.

Let’s grant that in the early Christian population, “Junia” outnumbers “Junias” by a factor of 9:1. Let’s also generously grant that the uses of “famous among” where the individual is implied to be a member of the group outnumber the uses where the individual is merely known to the group by a factor of 9:1. One might think that this yields a probably of 0.9 × 0.9 = 0.81 that the text affirms Junia/s to be an apostle.

But that would be to commit the infamous base rate fallacy in statistical reasoning. We should think of a text that praises a Junia/s as “famous among the apostles” as like a positive medical test result for the hypothesis that the individual praised is a female apostle. The false positive rate on that test is about 0.19 given the above data. For to get a true positive, two things have to happen: we have to have Junia, probability 0.9, and we have to use “among” in the membership-implying sense, probability 0.9, with an overall probability of 0.81 assuming independence. So the false positive rate on the test is 1 − 0.81 = 0.19. In other words, of people who are not female apostles, 19 percent of them will score positive on tests like this.

But we have very good reason to think that even if there were any female apostles in the early church, they are quite rare. Our initial sample of apostles includes the 12 apostles chosen by Jesus, and then one more chosen to replace Judas, and none of these were women. Thus, we have reason to think that fewer than 1/13 of the apostles were women. So let’s assume that about 1/13 of the apostles were female. If there were any female apostles, they were unlikely to be much more common than that, since then that would probably have been more widely noted in the early Church.

Moreover, not everyone that Paul praises are apostles. “Apostle” is a very special position of authority for Paul, as is clear from the force of his emphases on his own status as one. Let’s say that apostles are the subjects of 1/3 of Pauline praises (this is something that it would be moderately easy to get a more precise number on).

Thus, the chance that a randomly chosen person that Paul praises is a female apostle even given the existence of female apostles is only about (1/13)×(1/3) or about three percent.

If we imagine Paul writing lots and lots of such praises, there will be a lot of Junia/s mentioned as “famous among the apostles”, some of whom will be male, some female, and some of whom will be apostles and some not.
All of these are the “positive test results”. Of these positive test results, the 97% percent of people praised by Paul who aren’t female apostles will contribute a proportion of 0.19 × 97%=18% of the positive test results. These will be false positives. The 3% people who are female apostles will contribute at most 3% of the positive test results. These will be true positives. In other words, among the positive test results, approximately the ratio 18:3 obtains between the false and true positives, or 6:1.

In other words, even assuming that some apostles are female, the probability that Junia/s is a female apostle is at most about 14%, once one takes into account the low base rate of women among apostles and apostles among those mentioned by Paul.

But the numbers above are made-up. Someone should re-do the analysis with real data. We need four data points:

  • Relative prevalence of Junia vs. Junias in the early Christian population.

  • Relative prevalence of the two senses of “famous among” in Greek texts of the period.

  • Reasonable bounds on the prevalence of women among apostles.

  • Prevalence of apostles among the subjects of Pauline praise.

And without such numbers and Bayesian analysis, I think scholarly discussion is apt to fall into the base rate fallacy.


T said...

The Lexicon of Greek Personal names gives seven results for the name Ιουνια, all dating to the imperial era. It gives 0 results for Ιουνιας. However, these are Roman names so you would also need to check the Latin results.

Alexander R Pruss said...

Interesting. Even if one ups the Junia ratio to 100%, if one fixes the other numbers, one still gets that it's significantly less than 50% likely that she's an apostle.

Aron Wall said...

Your post is missing any discussion of what the term "apostle" actually meant to the early Christians. I think it is clear that it was used both in a narrower and a broader sense. In the narrower sense of the word, only the Twelve qualified, and none of them were women.

The broader definition was any person who was a direct witness to Jesus' Resurrection. It is in this sense that Paul vigorously defended his own claim to be an apostle, although his apostleship was abnormally timed since Jesus did not appear to him until after the Ascension. But using this definition, the category manifestly includes women, e.g. Mary Magdalene, and in fact I would expect the number of female apostles to be not enormously different from 1/2, given that Jesus' Resurrection appearances included some to large groups of people, which would most naturally have included both sexes.

Alexander R Pruss said...

The sense of "apostle" that I am interested in seems to me to be neither. It includes *authority*: when Paul talks of his being an apostle, that may include being a witness, but it centrally includes his special apostolic authority. But it goes beyond the 12.

Aron Wall said...

That may be the sense of "apostle" that you are most interested in, but it is only relevant to the interpretation of Rom 16:7 if that was the meaning that Paul had in mind. Anyway as I read him Paul seems to have based his claim to authority primarily on his status as a witness to Christ and his gospel. But as a Protestant I probably have very a somewhat different conception of ecclesial authority than you do...

Alexander R Pruss said...

To be more precise, I am very much interested in whether Paul considered a woman to be an apostle in the authority sense. I am not much interested in whether Paul considered a woman to be an apostle in the witness sense.