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Alicorn comments on Taking the awkwardness out of a Prenup - A Game Theoretic solution - Less Wrong
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Right. The intended signal is "I am so sure that I will not cheat (at least with the particular result of a child) that I don't mind guaranteeing I'll get caught if I do".
The phrase between parentheses is a critical issue, since it is extremely easy - and, in fact, the default - to cheat without producing illegitimate offspring, thus making the prenup fairly worthless.
It's actually likely to make things worse, since swearing that "I will not cheat and get pregnant" is going to bring one's attention to the backdoor - i.e. that you never promised not to cheat outright. It looks like a classical and extremely clumsy deception.
Unless, that is, you'd be happy with your husband being suspicious of you at the same time he is confident that his child is really his.
Of course I would also promise not to cheat outright; this just doesn't have the convenience of being so easily verifiable.
It seems like a reasonable way to signal fidelity in advance. Guys can do paternity tests pretty easily these days - if they have doubts - though... and girls realise that. So, maybe this doesn't buy you that much - in practice.
The point is not to wait until there are doubts. Getting to the point of actionably strong doubts is half the problem.
If there are to be doubts they will probably begin before birth - when testing is not practical. Testing after the doubts begin seems to be a pretty likely outcome.
Also, I figure the guy is going to want to be the one who administers any paternity testing. A test administered by the girl leaves some opportunity for deception by switching samples.
Testing to resolve uncertainty over paternity seems like a good case of humans consciously and deliberately caring about the welfare of their genes. Some seem to think that evolution's motivation for a man to reproduce his genes comes is in the form of sexual desire and pleasure - but for many, this is just not so.