This is the part of his explanation I find confusing too, though I do agree with his general argument: the results aren't really useful when they haven't been tested on a dataset representative of the real distribution.

From what I can gather he's basically saying that the "probability of a random face being classified as homosexual" is 0.5. This isn't REALLY true (would have to run the classifier on all possible faces to find this), but that is in fact the "environment" the classifier has been trained within.

If the test set of images really were 50/50 and the human judges weren't told that, then they were effectively given inaccurate priors, which would obviously reduce their accuracy.

I guess because the algorithm has been trained on 50% straight 50% gay and the 80% figure is actually for telling appart a pair of straight and gay persons, it will say gay half the time.. But this is confusing you are right. The explanation using false positive is clearer.

If there is 1000 persons, 40 gay, and the algorithm is 80% accurate, it will say: 960 * 20%= 192 straight people are gay and 40 * 80% = 32 gay person are gay. Not very impressive and shows a very stong gay bias if I can say so