Derk Pereboom's four-case argument demonstrates that parity reasoning forces compatibilists to either accept the manipulated agent is free or deny freedom to the ordinary determined agent.

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Compatibilists(as used in philosophy of free will): Philosophers who believe that free will and determinism (the idea that everything is predetermined) can both be true at the same time, rather than being opposites.
Derk Pereboom(as a key philosopher defending this position): A contemporary philosopher who defends hard incompatibilism and argues that people cannot be truly morally responsible for their actions.
Determined agent(The ordinary person in Pereboom's argument): A person whose actions are the inevitable result of prior causes (like physics determines how a billiard ball moves after being hit), though the person isn't aware of this causation.
Four-Case argument(Pereboom's version of the manipulation argument): Pereboom's manipulation argument that compares four cases of the agent Plum deciding to kill White, ranging from direct neuroscientist manipulation to ordinary causal determinism, arguing there is no free-will-relevant difference between them

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