If I might mention, in my experience it's not so much the men choosing the women, but the women choosing the men. I strongly remember how back in the 1980's, the Japanese economy was booming and wealthy Japanese men were buying up everything in sight. Suddenly it was common to see a buxom blonde clinging on to wealthy Japanese magnates.
It doesn't have to be the uber-wealthy, either. In the military it's common for women from poorer countries to do their utmost to wind up married to American servicemen.
To be sure, it's not always the women choosing the men - as if the modern world was some kind of perpetual Sadie Hawkins Day - but we shouldn't think it's only the men who do the choosing, or that if they do choose, that it has anything to do with race.