How to model user choice probability: binary model vs multi class model
This is a textbook multi-armed bandit problem where Morpheus needs to learn the correct policy about offering pills. As you’ve said the Neos are independent, and making the assumption that there is a best pill overall, we need an algorithm that will experiment with each of the pills to find out which one is most likely to be accepted. This is the same as having three one armed bandit slot machines and trying to find out which one will pay out most frequently.
In the case where the Neos are observable (so that we have some information about each Neo and can predict what pill they would like based on their characteristics) this becomes a contextual bandit problem. This is the basic form of reinforcement learning problems
In a contextual bandit problem, you need to balance exploration (trying out offering different pills to different Neos to find out what they like) with exploitation (choosing what seems to be the best pill based on what we saw so far). This is why straight-up supervised multinomial classification approaches (as in e.g. Benji Albert’s answer) will struggle to converge: they don’t explore the “action space” (i.e. try out a bunch of responses) sufficiently in order to generate a variety of training examples for themselves.