Re: Loving: A Toy Model

sigidunum@xxxxxxxxx wrote:

Last week marked the 40th anniversary of _Loving v. Virginia_.
_Loving_ was the landmark Supreme Court decision that held that
individual states could not prohibit marriage between persons of
different races. (1)

Since then, mixed marriage in the US has grown steadily, from about
0.2% in 1970, to 2.2% in 1990, to around 7% today. In 1970, only one
couple in 500 was walking up to the altar with someone of a different
race; today it's about one in 14.

One result of this, naturally, is a growing number of people who
consider themselves of no particular race. Starting in 1990, the US
Census added a box for "multiracial/mixed". Currently about 6.8
million Americans self-identify as such, or a bit over 2% of the
population.

So, where will this take us?

I'd like to run a toy model with the following assumptions.

Racial composition of the US at start: White 70%, Hispanic 12%, Black
12%, Asian 4%, Mixed 2%. (2)

Assume discrete generations. In the first generation, intermarriage
is 7%; in the second, it's 10%; in subsequent generations, it
stabilizes at 12%. (3)

Children of a mixed marriage will have a 1/3 chance to identify with
either parent, and 1/3 chance to self-identify as "mixed".

Now: I suspect that the smaller groups will start to shrink after the
first couple of generations, while the "mixed" category will grow
quickly and then stabilize. But I lack the programming skills to run
this thing. Is there anyone out there who could set up a quick
script? I'm curious to see where this would go.

ISTR a very similar scenario that was well modeled by repeated multiplications of 3x3 matrices. (Dim) memory dredges up the words "stochastic equilibrium"

The linear algebra book I recall seeing that in is at the Glendale library, I'll try to pick it up next time I go there.

Hop
.

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