Yeah, I remember the part about Xd beating out X, but that surely implies that Xd codes for a protein that is expressed in 75% of XXd women, 97% of XdY men and 100% of XdXd women, and that this protein is in some way significant. But we clearly see that Carmela is not in any way disadvantaged by this protein, and nor are the huge number of other people who also express it (if we take the comment that every female has at least one copy of this gene literally, then at least 75% of the female population expresses Driver-X, without any negative effects worth mentioning). It's possible, I suppose, that the Driver-X protein interferes in some lethal way with the development of males, but other than the fact that there are very few males, I don't remember anything in the story that would connect the two - if someone can dig out a line that makes it explicit, please let me know.
Everyone else seems to interpret it as meaning that an XdY fœtus has a 97% chance of developing as female, though; is that correct? If so, it leads to some interesting conclusions, but given a concerted effort at controlled breeding (which is explicitly happening), it doesn't lead to a shortage of males.
First of all, all those XdY females are basically suffering from a variation on
Turner Syndrome, except perhaps without the infertility - after all, only XdXd women for not allowed into the breedatoriums (literally not allowed through the doors? I'd assumed that was the kind of simplification you'd tell a child...). Actually, depending on what it meas by "beats out", maybe 75% of XXd females are also suffering from Turner...
Anyway, if you have an XXd mother, you separate out the father's Y chromosome sperm, and only use that. That gives you a 50% chance of XY (male), 48.5% chance of XdY (female) and a 1.5% chance of XdY (male). If XdY females are fertile, you use the father's X chromosome (not using any sperm from XdY males), and you have a 50% chance of XY (male) and 50% chance of XXd (female). So half of all children born are male, assuming you can't separate out eggs be sex chromosome the way you can sperm. After a generation or so, when the male population is once again too large to be contained (say, about the time this story is set), there are some policy decisions to be made about how to make sure the male population stays stable, but that's not an insurmountable one, and so long as the controlled breeding centres are producing enough males for their own use, it's frankly immaterial, as society can clearly remain stable and vibrant with only the number of males that they currently have.