Eliezer says the data shows that Overweight and Internet both make exercise less likely.
I don’t think he actually says that? He just says they both causally affect exercise:
Which says that weight and Internet use exert causal effects on exercise, but exercise doesn’t causally affect either.
[EDIT: I’m totally, wrong, he does say “we now realize that being overweight and spending time on the Internet both cause you to exercise less”]
Regarding your second point:
That would imply that P(O|I & not E) should be less than P(O|not E); and that P(I|O & not E) should be less than P(I|not E).
FWIW, I don’t take the sentence “overweight and internet both make exercise less likely” to imply that—just to imply that p(E | O) < p(E | not O) and p(E | I) < p(E | not I). The interaction terms could be complicated.
It is weird that I is independent of O given not E, given that from that graph you wouldn’t expect conditional independence, but I is not independent of O given E, so that’s OK and consistent with the graph.
I don’t think he actually says that? He just says they both causally affect exercise:
[EDIT: I’m totally, wrong, he does say “we now realize that being overweight and spending time on the Internet both cause you to exercise less”]
Regarding your second point:
FWIW, I don’t take the sentence “overweight and internet both make exercise less likely” to imply that—just to imply that p(E | O) < p(E | not O) and p(E | I) < p(E | not I). The interaction terms could be complicated.
It is weird that I is independent of O given not E, given that from that graph you wouldn’t expect conditional independence, but I is not independent of O given E, so that’s OK and consistent with the graph.