Pereboom distinguishes two libertarian positions, agent-causal and event-causal. While his agent-causal positions involve metaphysical freedom if not immaterial substance, his event-causal views assume that indeterminism is the direct or indirect cause of the action. He then traces decisions determined by character back to early character-forming events. Since they are always in turn either themselves determined, or at best indetermined, we can not be responsible for our characters either. This is the same regress as in Galen Strawson's Basic Argument.

According to the libertarian, we can choose to act without being causally determined by factors beyond our control, and we can therefore be morally responsible for our actions. Arguably, this is the common-sense position. Libertarian views can be divided into two categories.

In agent causal libertarianism, free will is explained by the existence of agents who can cause actions not by virtue of any state they are in, such as a belief or a desire, but just by themselves — as substances. Such agents are capable of causing actions in this way without being causally determined to do so. In an attractive version of agent-causal theory, when such an agent acts freely, she can be inclined but not causally determined to act by factors such as her desires and beliefs. But such factors will not exhaust the causal account of the action. The agent herself, independently of these factors, provides a fundamental element. Agent-causal libertarianism has been advocated by Thomas Reid, Roderick Chisholm, Richard Taylor, Randolph Clarke, and Timothy O'Connor. Perhaps the views of William of Ockham and Immanuel Kant also count as agent-causal libertarianism.

In the second category, which I call event-causal libertarianism, only causation involving states or events is permitted. Required for moral responsibility is not agent causation, but production of actions that crucially involves indeterministic causal relations between events. The Epicurean philosopher Lucretius provides a rudimentary version of such a position when he claims that free actions are accounted for by uncaused swerves in the downward paths of atoms. Sophisticated variants of this type of libertarianism have been developed by Robert Kane and Carl Ginet.
(Living Without Free Will, p.xv)

On Ginet's and Kane's conceptions, are free choices indeed partially random events (or perhaps even totally random events on Ginet's account) for which agents cannot be morally responsible? At this point, one might suggest that there is an additional resource available to bolster Ginet's and Kane's account of morally responsible decision. For convenience, let us focus on Kane's view (I suspect that Ginet's position will not differ significantly from Kane's on this issue). One might argue that in Kane's conception, the character and motives that explain an effort of will need not be factors beyond the agent's control, since they could be produced partly as a result of the agent's free choices. Consequently, it need not be that the effort, and thus the choice, is produced solely by factors beyond the agent's control and no further contribution of the agent. But this move is unconvincing. To simplify, suppose that it is character alone, and not motives in addition, that explains the effort of will. Imagine first that the character that explains the effort is not a product of the agent's free choices, but rather that there are factors beyond his control that determine this character, or nothing produces it, or factors beyond his control contribute to the production of the character without determining it and nothing supplements their contribution to produce it. Then, by incompatibilist standards, the agent cannot be responsible for his character. But in addition, neither can he be responsible for the effort that is explained by the character, whether this explanation is deterministic or indeterministic. If the explanation is deterministic, then there will be factors beyond the agent's control that determine the effort, and the agent will thereby lack moral responsibility for the effort. If the explanation is indeterministic, given that the agent's free choice plays no role in producing the character, and nothing besides the character explains the effort, there will be factors beyond the agent's control that make a causal contribution to the production of this effort without determining it, while nothing supplements the contribution of these factors to produce the effort. Here, again, the agent cannot be morally responsible for the effort.

However, prospects for moral responsibility for the effort of will not improved if the agent's character is partly a result of his free choices. For consider the first free choice an agent ever makes. By the above argument, he cannot be responsible for it. But then he cannot be responsible for the second choice either, whether or not the first choice was character-forming. If the first choice was not character-forming, then the character that explains the effort of will for the second choice is not produced by his free choice, and then by the above argument, he cannot be morally responsible for it. Suppose, alternatively, that the first choice was character-forming. Because the agent cannot be responsible for the first choice, he also cannot be responsible for the resulting character formation. But then, by the above argument, he cannot be responsible for the second choice either. Since this type of reasoning can be repeated for all subsequent choices, Kane's agent can never be morally responsible for effort of will.

Given that such an agent can never be morally responsible for his efforts of will, neither can he be responsible for his choices. For in Kane's picture, there is nothing that supplements the contribution of the effort of will to produce the choice. Indeed, all free choices will ultimately be partially random events, for in the final analysis there will be factors beyond the agent's control, such as his initial character, that partly produce the choice, while there will be nothing that supplements their contribution in the production of the choice, and by the most attractive incompatibilist standard, agents cannot be responsible for such partially random events.
(Living Without Free Will, p.48-50)

In a contribution to Essays on Free Will and Moral Responsibility, edited by Nick Trakakis and Daniel Cohen, 2008, Pereboom summarizes his case for "Hard Incompatibilism,"

Here Pereboom uses the standard agrument against free will

According to the hard incompatibilist position I advocate, we would not have the sort of free will required for moral responsibility if determinism were true. We would also lack this sort of free will if indeterminism were true and the causes of our actions were exclusively states or events. If the causes of our actions were exclusively states or events, indeterministic causal histories of actions would be as threatening to this kind of free will as deterministic histories are. However, it might well be that if we were undetermined agent-causes — if we as substances had the power to cause decisions without being causally determined to cause them — we would then have this sort of free will. But although our being undetermined agent-causes has not been ruled out as a coherent possibility, it is not credible given our best physical theories. Thus we need to take seriously the prospect that we are not free in the sense required for moral responsibility.

Pereboom does not see that some event acausality must be a prerequisite for the agent causality he says might be a coherent description of free will.

Genuinely random, uncaused events could contribute to alternative possibilities for thoughts and actions. But Pereboom does not think alternative possibilities are needed for moral responsibility.

He introduces a technical distinction between source and leeway incompatibilism that parallels John Martin Fischer's distinction between the actual sequence of events in a decision and any alternative sequences that depend on the existence of alternative possibilities. Fischer says the alternative possibilities may generate "flickers of freedom," But he seems convinced by Harry Frankfurt's thought experiments that show alternative possibilities are not needed to establish free will.

Pereboom says:

In metaphysical terms, the sort of free will required for moral responsibility does not consist most fundamentally in the availability of alternative possibilities, but rather in the agent’s being the causal source of her action in a specific way. Accordingly, I advocate source as opposed to leeway incompatibilism.
(Essays on Free Will and Moral Responsibility, p.1)

The Four-Case Argument is only meant to enhance the intuition of lost agential control, in order to support the fundamental Determinism Objection in the standard argument against free will.

Since the manipulators are only hypothetical and unreal, Pereboom uses them only to lend weight to the case for hard incompatibilism, which he defends whether or not determinism is true since he is agnostic.

In Case 1 evil neuroscientists build a humanoid with remote radio controls in its brain and cause it to murder someone. In Case 2 they create a humanoid with a computer for a brain and program it to be a murderer. In Case 3 a real human is conditioned by rigorous behavior modifications to become a murderer. And in Case 4 the murderer is a normal human being who grew up in a world where physical determinism is true, so becoming a murderer is the end result of reason-responsive deliberations.

Pereboom wants us to transfer our likely conclusions that the agent is not responsible in Cases 1-3 to Case 4, where ultimate causes for the agent's action are traceable to events beyond his control, what Pereboom calls the Causal History Principle.

Pereboom's clever argument seems unlikely to convince confirmed compatibilists who already are comfortable with causal determinism. They know how to excuse moral responsibility in the case of real manipulations or other non-agential factors like coercion, addiction, hypnosis, etc.

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