This is the gist of the Rational Expectations wave of economic theory.

https://www.nobelprize.org/prizes/economic-sciences/1995/cer...

Consider the problem of predicting an agent's binary choice. If an agent follows a strategy of always choosing the opposite of what the algorithm predicts, then the algorithm's prediction will always be incorrect. A "true future predicting algorithm" cannot correctly predict the actions of certain kinds of agents, as long as those agents can observe the prediction.

There will always be probability involved, the algorithm’s job will be also be to “wrap the prediction” in a way receiver thinks will it will benefit from ( negotiate ) . Hence leading to following the prediction.

Hari Selden had a pretty developed concept what people can know about an algorithm that anticipates their behavior.

They got mad ?

"Violence is the last refuge of the incompetent." - not actually Hari Seldon

In physics, I believe this is called the observer effect.

Indeed, shouldn't that be the point?

Yes, but that would make it infinitely hard for the algorithm as the output is depending on who is receiving the output. Hence the algorithm should have perfect understanding of environment, receiver and equation between the environment and receiver.