No spoilers for recent episodes (I mention last night's, but it's not new information). Only a slight spoiler if you're so far behind that you don't know that someone in Game of Thrones is guilty of incest.
In last night's episode of Game of Thrones, Tyrion tells Cersei that she "beat the odds" because two of her three children are sane (it was always said the Targaryen children of incest had a 50/50 chance of insanity). As I reflected on this exchange between brother and sister, it occurred to me that she beat another set of 50/50 odds by having two boys--it is best, after all, to have both an heir and a spare. Of course, she herself came from a family with two boys and one girl... And Catelyn and Ned Stark were similarly lucky, with three sons and two daughters. This set me off, tallying sons and daughters in the most powerful noble families of Westeros. Some I knew off the top of my head, but I was able to fill in gaps thanks to George R. R. Martin's comprehensive appendices on the noble families of Westeros. The results were quite surprising.
Here is my tally. I only looked at the most prominent families (sorry, Florents and Freys), and I included two generations where the information was accessible--in general, this came down to the children of the current (or recently deceased) lord of each great house, plus the children of that lord's father (including the current lord himself).
Stark (Eddard): 3 boys/2 girls; Stark Sr.: 3 boys/1 girl
Lannister (Tywin): 2 boys/1 girl; Lannister Sr.: 4 boys/1 girl
Tully (Hoster): 1 boy/2 girls; Tully Sr.: 2 boys/0 girls
Targaryen (Aerys): 2 boys/1 girl
Baratheon (Robert...): 2 boys/1 girl; Baratheon Sr.: 3 boys/0 girls;
Baratheon (Stannis): 0 boys/1 girl
Tyrell (Mace): 3 boys/1 girl; Tyrell Sr.: 1 boy/2 girls
Martell (Doran): 2 boys/1 girl; Martell Sr.: 2 boys/1 girl
Greyjoy (Balon): 3 boys/1 girl; Greyjoy Sr.: 4 boys/0 girls
Arryn (Jon): 1 boy/0 girls
Total: 38 boys/16 girls
Wow. Yes. It would appear that the noble houses of Westeros produce more than twice as many boys as girls. Now it's possible that the appendices didn't bother to mention noble children who died very young, though that group should include approximately equal numbers of boys and girls. It is also possible that the appendices left out sisters who married less important families and thus don't matter much anymore, but overall the appendices are pretty good at reporting marriages as well as deaths (at most, I think there could be girls missing from the Tully Sr., Greyjoy Sr., and maybe Martell Sr. counts). If you see any errors above, please let me know. Still, I find it highly unlikely that any of these sources of error could account for 22 missing girls.
This statistic stands out to me because I was recently reading some articles about the disturbing gender imbalance in parts of Asia (largely in China, but also in India and some other countries) due to gender-selection abortions (one such article: Asia's 163 Million Missing Girls). The noble families of Westeros look like an extreme version of that. But even if the maesters of Westeros have some sort of potion to induce a safe abortion, I'm pretty sure they don't have ultrasound capabilities to allow the identification of an unborn baby's gender. Is it possible that the nobles of Westeros are killing off newborn daughters? Extremely unlikely. First of all, the scandal would surely have gotten out. Second, daughters are useful for forming alliances through marriage. Third, the great noble houses have plenty of money, resources, and household staff, so extra children would not be a burden. If you get a girl, just try again for a boy. Every healthy born baby is an asset.
So what then caused this gender imbalance? I can only think that it is divine providence. I don't mean that praying to the Seven, the Old Gods, the Lord of Light or the Drowned God will give you more sons than daughters (who knows, maybe it will). I'm talking about the god of A Song of Ice and Fire, George R. R. Martin himself. He may not have been aware of it, but as he made up characters for his books, he simply wrote a lot more men into the noble families of Westeros than women. I can guess how this could have happened unintentionally. Martin created a story with a great collection of outstanding female characters. They are particularly outstanding because they live in a society where women have to work hard for influence, so most women end up playing the meek wife. Such meek women are less useful for a narrative than a knight swearing fealty and going into battle. Marrying a daughter off seems less urgent than arranging for succession of a lordship. Not to mention, the men kill each other quickly enough that they need to have a few spares written into the series.
Nicholas Eberstadt, a demographer at the American Enterprise Institute in Washington, said something for the article mentioned above that helps shed a little light on this situation of gender imbalance: The normal ratio should be 103 or 104 boys for every 100 girls. Over 107 starts to look suspicious, and over 130 is "sci-fi land".
So I guess that solves it. With an equivalent ratio of 237 boys for every 100 girls, we're in fantasy land.