What's expected of us is a story by Ted Chiang. It's very short so just go ahead and read it here so you understand what I'm talking about.

Did you read it? Good. I both love and hate this story because unlike other stories of killer ideas the exact concept is so clear. Agency in our choices is an element of typical human experience regardless of whether physics says the universe is a completely deterministic game of subatomic billiard balls or a stochastic mess of super positions. The fact that some metaphysical gate keeper isn't detectable is not an impediment to our perception of choice. So the idea that a repeatable example might be enough to push us over the edge into seeing ourselves as meat puppets turning us catatonic sounds chillingly plausible as far as killer info goes, and yet ...

How exactly does the predictor constrain peoples behavior? It's easy to imagine a world where the predictors are always right but it's a lot harder to imagine why they always have to be right. Here is a simple experiment anyone with a negative time delay circuit can do at home. Attach an electric motor to a breaker switch such that the motor's activation will break the circuit. Now rout the power supply for the motor through the breaker, into the negative time delay circuit, and into the motor. Watch as the motor cuts off it's own power supply thus preventing it from ever breaking the circuit and allowing it to kill it's own power before it was ever turned on. Hm ... I think I just simplified the grandfather paradox down to a circuit diagram. Regardless of whether the circuit is broken or the motor fails to turn on the entire mess shows that normal cause and effect just fail when applied to time travel. But wait, I hear you say, people aren't circuit breakers. Would the same rules apply to us? Well if they didn't then that would mean that we (and perhaps conscious minds in general) are a special case that keep the timeline consistent where less complex mechanisms create a blather of paradoxes.