The Incidence of Cuckoldry in Large Families

Earlier this week, Alkibiades posted a little blog on the probability of cuckoldry. Using a simple mathematical formula, he calculated the odds of a child being born as a result of a woman's sexual infidelity, and created a table with the statistical likelihood of a man being cuckolded, based on number of children in his family. Here is the final probability table:

1 child = 10% or 9:1 odds
2 children = 19% or 4.3:1 odds
3 children = 27% or 2.7:1 odds
4 children = 34% or 1.9:1 odds
5 children = 41% or 1.4:1 odds
6 children = 47% or 1.1: odds
7 children = 52% or 0.9:1 odds
8 children = 57% or 0.7:1 odds
9 children = 61% or 0.6:1 odds
10 children = 65% or 0.5:1 odds

Immediately after looking at his model, something struck me. For any model to be useful, it must bear some correlation to the real world. To the degree that a model correctly describes what is actually seen in the world, the model has validity. If a model makes predictions that widely diverge from what is actually seen, then the model is rejected as being unreliable. Now, from a mathematical standpoint, if one accepts that there is a 10% for a single child to be conceived by another man, given the promiscuity of modern men and women, then the rest of the table is mathematically sound. However, though the model may be mathematically sound, it's simplicity is also its downfall, since it does not align with the evidence of reality.

While I might be willing to trust the reliability of the table up through four children, I believe that there is a significant factor that changes the likelihood of cuckoldry for all families that have more than four children. My first question in looking at this table was to ask whether it matched my experience of the real world. As I have ten siblings, my mother gave birth to eleven children. If you use Alkibiades' model to determine the probability of cuckoldry with eleven children, then you will find that it would predict a 68% chance that one of my siblings was conceived due to sexual infidelity. I know for a fact that this is not the case. Now, it is certainly possible that Alkiabiades' model is correct and that my father is simply a lucky man, who happened to get lucky despite the fact that his outcome was statistically unlikely (32% chance). But, I have an alternate explanation.

My conjecture is that the sorts of women who are likely are be sexually unfaithful are also the sorts of women who are less inclined to have more than four children. The corollary to such a conjecture is that those women who choose to actually have five or more children are more likely to be sexually faithful than those who have four or fewer. I have a couple major reasons for this conjecture. Based on my anecdotal experiences, I have noticed that large families (5+ children) both tend to be more religiously devout and tend to be much more likely to homeschool than smaller families. This twofold difference leads both to a greater likelihood of sexually faithful behavior due to a wife's character and moral standards, and fewer opportunities for a wife to be unfaithful given the amount of time that is consumed in homeschooling her children. As such, these sorts of women both meet fewer potential seducers, and are less likely to commit adultery with any potential seducers they do meet.

Now, conjecture is of little value unless it actually matches the evidence of reality. As such, I have wracked my brains and spoken with several people in order to determine how many large families we knew, and what the actual incidence of cuckoldry is in such families. While it is still a relatively small data pool, I have come up with a list of 9 large families that I can confidently declare have zero incidences of cuckoldry. There is one family with 5 children, one family with 6 children, two families with 7 children, three families with 8 children, one family with 9 children and then my own family with 11 children. Now, Alkibiades' model would predict that about 5 of these 9 families should expect to have at least one incidence of cuckoldry. There is only a 0.07% chance that all 9 families will consist of legitimate children, if his model is correct. Yet, they all do consist completely of legitimate children. This fact alone calls the validity of the model into question. Similarly, though there are some large families that I do not know for contain zero illegitiate children, there are no large families that I can think of (nor has anyone I've yet asked) that actually do have one or more children as a result of sexual infidelity.

Now, my purpose in writing this is not to criticize Alkibiades' model, but instead to help refine it. In his blog post he specifically notes: "Of course these computations assume that all women have the same chance of cuckholding, but I’m sure there are good women out there." While that disclaimer would seem to be a minor footnote, I think that because of the real-world difference seen in those women who have five or more children it seems to be a fairly major oversight. As such, I would postulate that a model that better fits with reality would be a cuckold probability chart akin to this one:

1 child = 10%
2 children = 19%
3 children = 27%
4 children = 34%
5 children = 30%
6 children = 25%
7 children = 19%
8 children = 13%
9 children = 08%
10 children = 05%
11 children = 03%
12 children = 02%

Readers: Of course, to test the validity of such a model beyond my pitifully small collection of anecdotal data, more reliable data is needed. I have been searching for sociological studies on large families, and data on the actual number of large families in America, sorted by number of childen, but have been largely unsuccessful. As such, I welcome any data that you can offer, either of an official sort, or even more anecdotal data. Do you know any large families who have one or more illegitimate children? Do you know any large families that you are certain contain no illegitimate children?