This is extracted from the article Self-fertilization of the book What if? of xkcd:
At first, I just simply think that the multiplier he mentions is just a convenient name of a system with arbitrary rules. However, after he says about the multiplicative identity, I think that this has a deeper root in math, and here stems the question.
Why do you have the multiplicative identity, when the product here is made from two multipliers? The multiplicative identity I know is the element $e$ satisfies $e\cdot x=x$. But from what I understand from the book, it is the $x\cdot y=e$, and it's not required to have $y=x^{-1}$. Further more, $e=1\in\mathbb{R}$, but $x$ and $y$ are not. He explicitly says that the stat is number.
So can this happens? Is is actually be true, or am I misread him?
This is a table of how the rule works (the X letter in SEX row is irrelevant, not a multiplier):
It is unclear why $1$, not $0$, is the identity, but yes, the product of both multiplier should be a number so that it can be multiplied with other numbers later on.
From the sample, it appears the scheme is that the value for each gamete can be a stat, or a multiplier. However both stats and multipliers are just real numbers.
My first thought is that when the gametes are combined, two stats combine to whichever stat is higher. A stat and a multiplier combine to the product of the two, and two multipliers combine to 1. The problem with this idea is that it doesn't explain why two Dexterities of 14 combine to 14, while two Intelligences of 14 combine to 15. Either there is a typo, or there is some addtional rule that treats Dexterity and Intelligence differently.
As for why two multipliers combine to 1 instead of 0. He evidently chose to do that because multipliers act by multiplying. But if there is nothing to multiply (because both entries are multipliers, not stats), then it defaults to the identity. Since these are about multiplying, it is the multiplicative identity that they default to.
In other words, it is a somewhat arbitrary choice he made to handle a weakness in his scheme. Since it is his scheme, he can make whatever choice he wants.