The catholic church has always had a complicated relationship with homosexuality.

The central claim of Frederic Martel’s 2019 book In the Closet of the Vatican is that the majority of the church's leadership in Rome are semi-closeted homosexuals, or more colorfully, "homophiles". 

So the omnipresence of homosexuals in the Vatican isn’t just a matter of a few black sheep, or the ‘net that caught the bad fish’, as Josef Ratzinger put it. It isn’t a ‘lobby’ or a dissident movement; neither is it a sect of Freemasonry inside the holy see: it’s a system. It isn’t a tiny minority; it’s a big majority.

At this point in the conversation, I ask Francesco Lepore to estimate the size of this community, all tendencies included.

‘I think the percentage is very high. I’d put it at around 80 percent.’

…

During a discussion with a non-Italian archbishop, whom I met several times, he confirmed to me: ‘Three of the last five popes are said to have been homophilic, some of their assistants and secretaries of state too, as well as most cardinals and bishops in the Curia.

Apparently, this view of the church leadership is not an original one, and it’s not a new one. It’s not even one posited by independent investigators or enemies of the church. A reformist monk in the 11th century(!) named Peter Damian wrote a book documenting the prevalence of homosexuality within the church leadership called The Book of Gomorrah. Damian’s was an internal observation and critique of various kinds of ecclesiastical corruption, centuries before the reformation. Conversely, Martel’s book is an inquiry from an outside observer by way of long and exhaustive interviews, centuries after the reformation.

The Fraternal Birth Order Effect (FBOE) is a demographic observation that homosexual men are disproportionately likely to have older male siblings in populations for which sufficiently detailed data exists. The modern father of this literature is Ray Blanchard; he came up with the initial quantitative estimates of this effect in the 1990s. The maternal immune explanation for this has been written about before on LW and Scott's written about it well on several occasions. If Damian and Martel are correct, under some not particularly severe assumptions, the FBOE predicts high ranking church prelates will be lower ranking in birth order than expected by chance. The rest of this post will be a statistical and demographic investigation into this claim. 

Background

Given the power of gigantic modern datasets and analysis methods, it looks like Blanchard and his acolytes screwed up the statistics a bit, but were directionally correct. Recently, Ablaza et al. did a sophisticated analysis on 9 million people in the Netherlands and replicated the main finding. They also find the effect is not restricted to older brothers, but applies to all older siblings, and the effect is not restricted to men, but applies to women as well; it’s just largest in men who have older brothers. Here is the summary of this complicated regression analysis.

Adding one younger sister to an existing sibship is associated with a 13.8% decrease in the probability of entering a same-sex union (OR = 0.87, p < 0.001); moving one place down the birth order while keeping the number of younger and older brothers fixed is associated with an 7.9% increase in the probability of entering a same-sex union (OR = 1.08, p < 0.001); and replacing one older sister by one older brother is associated with a 12.5% increase in the probability of entering a same-sex union (OR = 1.13, p < 0.001).

So we have a rough estimate of  FBO effect over a large and modern dataset. Can we see something similar in a not quite as large, not as modern dataset?

Data

You wouldn’t believe what you can do with computers these days. Huge amounts of badly-structured information can quickly be compacted into giant, clean, legible rectangles of numbers. The Vatican keeps pretty detailed biographical information about their prelates, and a few millennia after the water turned into wine, selenium turned a bunch of shitty biographical sketches into clean biographical data of hundreds of cardinals spread over centuries.

Remember, Damian thinks homosexual leadership in the Vatican has been ongoing for centuries, and Martel claims

Homosexuality spreads the closer one gets to the holy of holies; there are more and more homosexuals as one rises through the Catholic hierarchy. In the College of Cardinals and the Vatican, the preferential selection process is said to be perfected; homosexuality becomes the rule, heterosexuality the exception.

So we need to be looking deep through time and at the highest levels of the Vatican, which is exactly the dataset I assembled. The most relevant biographical facts required to mount this analysis are how big cardinals’ families were and their birth order in that family, when available. Most of those men came from very elite families. Most are nobles, with a lot known about their genealogy. Cardinals are the most accomplished and capable men in the entire catholic hierarchy; most of them are prominent enough to have wikipedia pages. They make the people who have climbed to the top of even large modern government bureaucracies look positively junior varsity.

In addition to keeping secrets, the catholic church is also excellent at keeping records.

The final assembled dataset looks something like this.

In total, we have 921 cardinals with some sibship size information, 792 with some birth order information, and 638 with definitive information about both. The data goes from the 15th century into the 21st century. I’ve checked in the data and the code I wrote to study it here.

Analysis

Suppose the FBOE is broadly observable in dispersed catholic populations, and suppose it’s biologically rather than socially-mediated. If Martel is right that 80% of the college of cardinals is actually not-so-secretly gay, we will observe cardinals late in birth order more often than expected by chance. 

There are multiple related ways of quantifying this, and to ensure the conclusions are robust, I’m going to break this into 3 separate analytical specifications. The statistics reported in this section exclude the chauvinist 15th and 16th centuries since the data look like sons are much more preferentially reported than daughters during those times, and we don’t want to screw up the analysis in that way.

Expected versus Actual birth order, with missing birth order

The way the data ends up being structured, we often know the size of a given cardinal’s family when we don’t actually know his birth order. One way we can exploit this defect and waste no data is to come up with an expected birth order among all the catholic families who produce cardinals.

                                      $E\left[\text{Birth Order}\right]={\sum }_{n=1}^{N}P(\text{Total Siblings}=n)\cdot \frac{n+1}{2}$

where N is the maximum number of offspring a catholic woman could possibly carry. In this specification, the probability mass function of the total sibship is estimated using all the data regardless of whether it has associated birth order data (hence “with missing birth order”). This expected birth order is calculated and can then be compared to the actual average birth order for the cardinals observed in the data. If the expected birth order is lower than the actual birth order, we could conclude the cardinals are lower in birth order than expected and the FBOE is in play.

The distribution of total siblings in these families is modeled as a negative binomial distribution.

Yes, devout catholic families who take it seriously enough to produce cardinals have a lot of children.

Using this negative binomial estimate’s pmf, the expected birth order for these cardinals is 3.68, and the average observed birth order is 3.31, which is the exact opposite of what a mostly gay Vatican combined with the FBOE would predict. These cardinals are actually older than you would expect compared to their siblings.

Expected versus Actual birth order, without missing birth order

Maybe there’s some weird relationship between when a cardinal’s birth order is being reported and how large his family size actually is. In this situation, we would not want to use all the sibship size data; we would only use sibship size when we know the birth order. This will remove any worry about selection bias at the expense of using less data. The only thing that changes here is the estimated pmf for the total sibship size.

Ugh. Using this specification, things actually get worse. The expected birth order increases further to 3.71.

Oldest sibling versus youngest sibling

Birth order can be complicated to correctly reason about, and maybe we’re missing something. Maybe birth order produces a weird effect in gigantic families. Let’s keep it simple: What’s the representation of oldest siblings among cardinals? What about youngest siblings?

22.3 percent of cardinals are reported as eldest children. That compares to 21.6 percent which are youngest children. Eldest children are still favored.

Discussion

Analytically combining the FBOE with a potentially closeted Vatican is a difficult synthesis. The literature on the FBOE is fundamentally based on linear regressions which model a relatively uncommon phenomenon: obligate homosexuality. It’s perhaps capable of answering how many more older siblings are needed to bump a man’s chances of being homosexual from 3 percent to 3.2 percent, but what if Martel is right and the Vatican is like a nightclub in Chelsea? How many more older siblings should patrons of the Chelsea nightclub have than all other men in New York? If the average guy on the street has a 3 percent chance of being gay compared to a guy in the nightclub who has an 80 percent chance of being gay, that’s an odds ratio of ~26. The regression coefficients in Ablaza et al. are all around 0.1, which means that the nightclub patrons are expected to have log(26) / 0.1 = 14.15 more older siblings than the man on the street, which is a stretch even if it’s a catholic gay nightclub.

Unfortunately, the FBOE only explains a small portion of how prevalent homosexuality is in large populations, but I still have a pretty strong conviction that if the FBOE is real and the Vatican is really closeted, we would be able to observe it in this data.

A few potential resolutions to this strange result:

1. The FBOE isn’t real, or it isn’t biologically mediated.
2. The Vatican isn’t all secretly in the closet.
3. I mentioned before that cardinals are all highly-educated men who have somehow made their way to the top of a giant bureaucracy, which is competence of a kind. If older siblings are actually more capable of that than younger ones, that could swamp any FBOE effect and make it invisible in the data.
4. I looked into the idea that elite families in past centuries would preferentially have their older children take an ecclesiastical path. In the biographical sketches there are even references for noble families preferentially grooming their second, but not their first sons to be clerics (“Luigi, the second son, was destined for a career in the church, unlike his older brother Mario who inherited everything”). However, the observed pattern of cardinals being older by birth order continues through modern times. Interestingly, there is evidence in the older data that second sons were preferred to be in the church compared to first ones.
5. There’s something about these giant families which diminishes the FBOE, though this doesn’t seem to make any sense, since I think most people involved in this literature believe the effect is cumulative.
6. Homosexuality in the church is a different mental phenotype than homosexuality outside of it, and the FBOE applies only to the latter.

Conclusion

I don’t see it. If the Vatican is secretly in the closet, it doesn’t appear in a long term dataset reported from an institution with a history of excellent record keeping. The fact that we’re looking at large and completed families keeps a lot of the issues that can come up studying birth order out of play. This is potentially an excellent dataset for studying this.

I was quite sympathetic to Martel’s thesis coming in and was impressed by the depth of work presented in In the Closet of the Vatican. Overall, pretty disappointed in the negative result