There was some discussion of genetics in the FF.net comments for Chapter 23; I'd like to continue that here.
Going purely by canon evidence, disregarding Harry and Draco's results, I would have inferred that magic was dominant, not recessive.
I assume that the magical population of Britain is much smaller than its nonmagical population, that the vast majority of magical children in Britain attend Hogwarts, and that the vast majority of Hogwarts students are British.
There are roughly a million 11-year-old Muggles in Britain. The number of Muggle-born witches and wizards in any given year at Hogwarts is counted in the dozens, at most. This puts the probability of any given child of nonmagical parents being magical at somewhere around 10^-8, which is plausible for a simple random mutation.
Wizard-born Muggles, on the other hand, are common enough that the word "Squib" was created to describe them. The level of understanding of genetics that Harry displays -- the level that Draco could have if he was paying attention, even -- is sufficient to realize that the frequency of Wizard-born Muggles falsifies the model they settled on.
What simple model describes both the canon evidence and the MOR!canon evidence (Harry and Draco's results)? The best I've come up with so far is "Eliezer falsified data to suit his preconceptions", which is distinctly unsatisfying. (This model will be verified if Chapter 23 is edited to make the percentage of Squib-born Wizards 75% rather than 25%, and it will be falsified if Harry and Draco eventually realize that their theory doesn't work.)
According to Eliezer, the "muggle-born" are in fact the children of people who have one copy of the magical gene (and thus are descendants of Squibs who were cast into muggle society.). That only one in ten thousand people in Britain (who are not wizards themselves) have a copy of the gene for magic is not that improbable.
Update: Please post new comments in the latest HPMOR discussion thread, now in the discussion section, since this thread and its first few successors have grown unwieldy (direct links: two, three, four, five, six, seven).
As many of you already know, Eliezer Yudkowsky is writing a Harry Potter fanfic, Harry Potter and the Methods of Rationality, starring a rationalist Harry Potter with ambitions to transform the world by bringing the rationalist/scientific method to magic. But of course a more powerful Potter requires a more challenging wizarding world, and ... well, you can see for yourself how that plays out.
This thread is for discussion of anything related to the story, including insights, confusions, questions, speculation, jokes, discussion of rationality issues raised in the story, attempts at fanfic spinoffs, comments about related fanfictions, and meta-discussion about the fact that Eliezer Yudkowsky is writing Harry Potter fan-fiction (presumably as a means of raising the sanity waterline).
I'm making this a top-level post to create a centralized location for that discussion, since I'm guessing people have things to say (I know I do) and there isn't a great place to put them. fanfiction.net has a different set of users (plus no threading or karma), the main discussion here has been in an old open thread which has petered out and is already near the unwieldy size that would call for a top-level post, and we've had discussions come up in a few other places. So let's have that discussion here.
Comments here will obviously be full of spoilers, and I don't think it makes sense to rot13 the whole thread, so consider this a spoiler warning: this thread contains unrot13'd spoilers for Harry Potter and the Methods of Rationality up to the current chapter and for the original Harry Potter series. Please continue to use rot13 for spoilers to other works of fiction, or if you have insider knowledge of future chapters of Harry Potter and the Methods of Rationality.
A suggestion: mention at the top of your comment which chapter you're commenting on, or what chapter you're up to, so that people can understand the context of your comment even after more chapters have been posted. This can also help people avoid reading spoilers for a new chapter before they realize that there is a new chapter.