This paper suggests that the arguments for compatibilism are invalid because they use incompatible definitions of causal determinism and free will, an illegitimate definition of free will, and a logical fallacy concerning free will and morality.
Compatibilism is the view that causal determinism is compatible with free will. However, different arguments for compatibilism imply different definitions of free will. Therefore, we need to examine the compatibilist definitions of causal determinism and free will...
Causal determinism is the view that the state of the universe at any given tiime is wholly determined by earlier states together with the laws of nature. Hence every event is causally entailed by antecedent events. This is reflected in the description of determinism as set out in an SEP article on compatibilism: 
...if determinism is true, there are (causal) conditions for that person's actions located in the remote past, prior to her birth, that are sufficient for each of her actions.
A compatibilist may argue that although the events in the remote past entail a chain of events, all of them are causally effective. Thus they would, legitimately, assert that causal determinism is compatible with causally effective will. I.e. Barring other constraints, our actions are caused by our willed choices. That sounds very much like saying that our actions are freely willed, but there is a difference, which we will establish in due course...
Compatibilists present a range of arguments for causal determinism being compatible with free will:
These imply three different definitions of free will, therefore we shall address them individually:
The claim of "liberty of spontaneity" goes beyond causal effectiveness as part of the causal chain. It asserts that we not only will our choices, but do so freely. We may illustrate the difference with an example of a computer running a conventional program:
Say I have a computerized machine for making my breakfast. I wish to alternately have have egg on toast or a bacon sandwich, so I write a short program for the machine:
Function Choose_Breakfast(egg_days) !--------- If egg_days < 1 make egg_on_toast increment egg_days Else make bacon_sandwich egg_days = 0 End If Return egg_days
I should explain that "egg_days" is a variable that is passed to the procedure each time it is run. It reflects the number of times I have had egg on toast on sequential days. So:
So each day the computer decides whether to make egg on toast or a bacon sandwich, and that choice is causally effective. The appropriate breakfast is made. But can that choice be deemed "freely willed"? Of course not. The computer has no freedom over the choices it makes. They are wholly determined by external factors. So the claim of "liberty of spontaneity" goes beyond causal efficacy of the will. It asserts that we have input to the factors that determine our choices, and hence have a degree of control over our actions.
Therefore, by this usage, the term "free will" requires that:
It can legitimately be said that compatibilist will is effective, and that "liberty of spontaneity" allows freedom. However the "liberty of spontaneity" requires that we have input to the factors that determine our choices, whilst causal determinism requires that the choices are wholly entailed by external factors. These requirements are mutually exclusive. So causally effective will and freewill are not synonymous. Hence, although this argument has legitimate definitions of causal determinism and free will, the definitions are incompatible with each other.
This argument suggests that free will equates to the absence of overriding constraints like:
The absence of overriding constraints and impediments is necessary for the will to be deemed free, but is it sufficient? What is absent from this list is entailment by prior events. So it is compatible with causal determinism, and is causally effective, but it lacks the "liberty of spontaneity" mentioned above.
By this argument, an act of will may be wholly entailed by external factors yet is deemed to be free. I would suggest that is an illegitimate use of the word "free". It conflates free will with causally effective will. So this argument achieves compatibility between causal determinism and what it calls "free will", but that definition of free will is illegitimate.
The argument that free will is a moral issue, independent of the presence or absence of a causal relationship, may have arisen because, under determinism, it does not necessarily follow that a person can act freely. This is illustrated by an extract from an SEP paper:
determinism implies that the only sense in which we are responsible for our actions is the sense in which a chess-playing computer is responsible for its moves
However, even if determinism is true, it may be deemed to be socially necessary to hold people responsible for their actions. Hence they may be deemed to have acted freely, in order that they may be held to be morally responsible. However, it does not follow that, because it is asserted that a person acted freely, that they did in fact do so. To conflate the two invokes a logical fallacy known as "asserting the consequent":
Although both a and b are true, c does not necessarily follow. Hence this argument fails because it is based on a logical fallacy.
The arguments for compatibilism are invalid because they respectively use:
 Stanford Encyclopdia of Philosophy - Compatibilism:
 Stanford Encyclopdia of Philosophy - Arguments for Incompatibilism: