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Kindly comments on Harry Potter and the Methods of Rationality discussion thread, February 2015, chapters 105-107 - Less Wrong
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The argument from number of descendants equally applies to the question "Why isn't every wizard in Britain, or none of them, a Parselmouth?" It does not make any particular feature of being a Parselmouth more likely.
.. I have a theory about that.
What is the number one piece of advice we give people about relationships? The one rule which is regarded as the key to success and happiness in romance?
Its honest communication.
Salazar's decendants can have a perfect, magically enforced, version of that. And all they have to do is marry their cousin. The family wasn't obsessed with blood purity at all, it is simply that after growing up in a household where harmony was routinely established via this glorious gift of Salazar, the very idea of intimacy with anyone that this could not be shared with was usually repugnant.
That's why Quirrel calls it a curse. It lead the entire clan down a path of inbreeding! Unintentional consequences are unintentional.
Canon!Salazar is a bloodpurist already. He and the other founders of Hogwarts have a big row about it- who should be able to attend Hogwarts? Only the pureblooded! Apparently this is the reason why he built the chamber of secrets in the first place... Awesome theory otherwise.
Perhaps — but in canon, Voldemort himself is not a pureblood. For that matter, his mother was not exactly raised to know how to have healthy relationships.
Riddle was born out of the near-final collapse of the bloodline. Grandparents were awful because of over 500 years of insularity and intermarriage. Mother whammies cute boy as escape tactic / because she's just seriously fucked up. But because his mother conceived him with someone not from the family, he ends up the first scion in, well, most likely centuries to be born with good health. Physically, anyway.
By all rights, Volde should be an inbred retard, not a genius dark lord.
That's not how inbreeding works, though... If one of your parents' family (in Voldie's case, his mother) has been inbred for generations but the other parents has a completely different gene pool, then you should be fine. Inbreeding just makes it more likely that you have two of the same recessive allelle (which is bad in many situations), but Voldie only got one of each from his mother.
I actually do understand genetics, but I forgot that Voldie had a muggle father. Been a long time since I read canon HP.
Unlike canon, Voldie's father in HPMoR could have lacked magical phenotype, but must have had one magic allele and at least some distant wizard/like ancestors, because of inheritance of magic in HPMOR (which is different from canon). If somebody sequenced the DNA of HPMoR version of Voldie's father, they would find the squib genetic make-up, not muggle.
That is just a side technical note, though. The father was probably sufficiently unrelated to the mother's family, which probably really helped with the inbreeding problems.
That is only if all deleterious alleles are recessive. Though of course, we don't have any numbers and can imagine anything.
ETA: and a single recessive deleterious allele in the father's genome would have disproportionate consequences. Although there would be about 50% chance of getting it, humans carry lots of such stuff, so overall probability of weak (but at least viable) progeny should still be high enough.
Inbreeding just makes it more likely you get two of the same allele (with bad consequences if said allele is deleterious), it does not make it inherently more likely that any single allele you have is deleterious.
True. And a progressively large portion of progeny would die before procreating, exactly because of that. Maybe there would even be bottlenecks along the way.
Yet it seems to me that a squib (?) whom Merope chose could have a different set of heterozygous=hidden deleterious alleles, which in Merope's genome would not have been eliminated yet, but getting close to it.
Also, how on Earth was Slytherin's curse even inherited? It would be something outside of genes, since he didn't know about their existence. So the ability would be develop undiminished with blood 'dilution', which means a Parselmouth cannot be seen as evidence of pure-bloodedness, which would be a blow to Draco's belief in his father's ethics... And in Harry's belief in genes-only inheritance...
Now, if Salazar was secretly a woman, and only daughters would get to be Parselmouths, that would be another story...