Friday, January 8, 2010

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?


  1. A few thoughts to consider:

    More children not only bring about more work, but also more witnesses to a crime. How likely is it a mother with a large family would manage to slip away unnoticed for an affair by both her husband and her large brood? There are days I sometimes have hardly enough time to shower between childcare, cooking, homeschooling, housework, homesteading work, and doing whatever else my husband needs done for the day...and we only have one living child thus far.

    Also to take into account is the fact that a mother with many children spends a fair portion of her life pregnant and/or breastfeeding. Both can cause a woman to be tired and also produce hormones that can decrease libido and some that cause bonding--with baby and husband. This reality may play a factor in these women being less likely to cheat as well. While we only have one child, due to a stillbirth and multiple miscarriages, I have been pregnant and/or breastfeeding for the better part of my marriage and can attest to the way this hormone cocktail works on the mind. Ancedotal I know, but something to consider.

    I'd also add the large families I know would support your thoughts.

  2. Nice insights, if anything, stated too hesitantly. I was going to say something along the lines of Hestia above. Women with that many kids are far less likely to cheat: they are older and less attractive, more busy, less social, more dependent on husband, more morally committed to family values, etc etc.

    Game-sters fixate on negative examples, and fall into the traps of selective attention bias. As I have said, Game is poison for a man's soul, as it corrodes your viewpoint about that world, especially women and family, as this bogus probability table indicates.

    In case you didn't notice, Alk's blog has a strong pro-evo-psych bias as well (which I slapped down once in the comment section back when I read it).

  3. Silas,

    To fix the table, you have to adjust the cuckold numbers for the smaller number of children upward to adjust for the downward adjustment at the high end of table.

    a small nitpick: how exactly did you verify to a "certainty" that there was no cuckolding? This isn't something that is widely advertised by the cuckolding women, further it would be something actively hidden.

    Not that you aren't probably more right than wrong in your assessment.

    Finally, Justin, other that saying you didn't agree with evo psych, nothing in any of your comments to our blog has ever approached being "slapped down" by you.

    I notice that despite that, you love psych terms like "Selection bias."

    As for poison for the soul, many of the great medicines in Western Civilization are derived from poisons and venom. You should be mindful to remember that despite your own, obvious biases.

  4. Justin, you left a drive by comment and never came back. You let your hatred of anything game related prevent you from seeing the sarcasm of that post.

    As Silas says at the end of this post and as I said as well, the assumption is that there is uniformity in the rate of cuckholdry by women. I'll spell it out even more clearly. By it's nature that's a false assumption, therefore the conclusion cannot follow.

    Have a nice day.

  5. The first model points to a distribution that assumes each trial (birth) is independent of the ones before and therefore has an equal chance of being a bastard. But paternity of childbirth is not a random event (at least for most people). A cheating whore of a wife is that way for all of her children while a virtuous wife is that way for all of hers. There are likely a few outliers of women who fell in with a bad crowd, too much to drink, never did it again, etc excuses, but the theory is sound.

    You would be courting violence to suggest that every 10th pregnant woman to appear at the delivery room was a lying whore.

    It therefore follows that a woman with 4 previous births with confirmed paternity would have a near zero chance of bastardy on the fifth trial and a nearly equal rate for additional deliveries. (shit happens).

  6. Social status is a large effect here. You will see much less cuckholding at higher social status levels than at lower.

  7. While I don't think Alkibades' model is correct; it's interesting to think about. Also, I'm glad he accounted for non-mutual exclusivity when figuring out the probabilities.

    He laid out a simple model that can now be worked on a tweaked in accordance with theory that Silas and Prof. Hale have pointed out to determine the true picture of cuckoldry.

  8. Silas,

    just a little nit pick. One child is 10% and 9:1 odds.

  9. A quick point:

    It is not the act of having many children, but the act of having many children while remaining married to the same man.

    In other words, I think the right model to consider this is really a decision tree of some sort.

    We have two potential cases with the birth of each child:

    1 - Husband's Child
    2 - Not Husband's Child

    And each occurrence of 1 should increase the odds of 1 occurring again.

    However, there is the other lurking assumption: assuming she is married to the same man the whole time. Merely looking at number of children will be insufficient, as it won't track serial marriage women or those who have children via multiple fathers while remaining single the entire time (both of which occur with a frequency greater than zero).

  10. Great thoughts everyone!

    @Hestia: I didn't even consider the implications of the fact that a woman with a large number of children spends a significant portion of her life pregnant/breast-feeding. Thanks for pointing that out!

    @Justin: While I will happily declare with certainty things that I am quite confident about, I also think it is foolish to boldly declare things that scientifically measurable unless one has a great deal of confidence concerning a model's correlation with reality.

    @Talleyrand: The certainty factor was something that I considered. For that reason, I trimmed my data pool somewhat. One thing is much more noticable in large families than in small ones is genetic similarity. With small families, you see a few similar features and several differences. With large families, you see genetic traits that are repeated in such a way that a child who is not genetically related to both father and mother would noticably stand out from the others. Because of the genetic support for legitimacy in addition to what is known about each of these family from close-knit social circles, I would posit a 98+% confidence in the validity of each of the 9 families that I included in the data set.

    For those families that I lack sufficient familiarity with, or am only 90% confident about, I chose to exclude from the data set.

    @Athol Kay: I completely agree. However, for at least several of the families in my data set, I would not consider the husband/father to be of high social status. Therefore, I would postulate that while on a broad scale, more cukoldry would occur at lower social status levels than at higher ones, people who are the sort who would choose to have large families should expect to see lower levels of cuckoldry even if the husband lacks Game or social status.

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