Presumably, if you use E to decide in Newcomb’s soda, the decisions of agents not using E are screened off, so you should only calculate the relevant probabilities using data from agents using E. If we assume E does in fact recommend to eat the chocolate ice cream, 50% of E agents will drink chocolate soda, 50% will drink the vanilla soda (assuming reasonable experimental design), and 100% will eat the chocolate ice cream. Therefore, given that you use E, there is no correlation between your decision and receiving the $1,000,000, so you might as well eat the vanilla and get the $1000. Therefore E does not actually recommend eating the chocolate ice cream.

Note that this reasoning does not generalize to Newcomb’s problem. If E agents take one box, Omega will predict that they will all take one box, so they all get the payoff and the correlation survives.

Presumably, if you use E to decide in Newcomb’s soda, the decisions of agents not using E are screened off, so you should only calculate the relevant probabilities using data from agents using E.

Can you show where the screening off would apply (like A screens off B from C)?

Presumably, if you use E to decide in Newcomb’s soda, the decisions of agents not using E are screened off, so you should only calculate the relevant probabilities using data from agents using E. If we assume E does in fact recommend to eat the chocolate ice cream, 50% of E agents will drink chocolate soda, 50% will drink the vanilla soda (assuming reasonable experimental design), and 100% will eat the chocolate ice cream. Therefore, given that you use E, there is no correlation between your decision and receiving the $1,000,000, so you might as well eat the vanilla and get the $1000. Therefore E does not actually recommend eating the chocolate ice cream.

Note that this reasoning does not generalize to Newcomb’s problem. If E agents take one box, Omega will predict that they will all take one box, so they all get the payoff and the correlation survives.

Can you show where the screening off would apply (like A screens off B from C)?