I work with the definition given by compatibilists
No, you seem to not, because every few days you come back spouting "no alternative actions" in a stunning flurry of syntax error.
Let me repeat that that construction of words, in ANY programming language at any point in time anywhere is a syntax error.
Programmers have, for every compiler that detects and rejects such errors, been forced to detect such orderings of words and make a warning that tells people about this and scolds them mechanically for even trying.
I wish we would just install a spell checker feature for people that detects "couldn't have done otherwise" and just red squiggles it with the explanation "modal error: apparent use of individual instance in place of type", particularly when attempting to speak to an individual instance rather than a type.
Sadly, though, because it is sometimes left ambiguous because of the informality of spoken English, they don't always get exposed in every instance; some instances would detect incorrectly without fully expanded syntax in the first place.
If the world does have random events, events that alter how things go, how would that help establish an argument for free will
We already explain this quite a bit: to the extent these "random" events (and I can't explain enough that you also do not have a coherent definition of randomness presented here or elsewhere), that to the extent this randomness exceeds the regularity of the nervous system, we would have to tolerate some manner of "sloppiness" among each other in our behavior, not because we all just claim a right to be a bit sloppy but because the universe itself has noise around the edges.
As it is, this kind of interaction of
non-correlated events, or
statistically independent events from the perspective of an outcome creeping in, we actually see something like this in reality in computational events: a transistor has a threshold region, where if the voltage is in a small boundary range on the transistor when the clock fires, it fires unreliably, unreasonably, in a way
also not correlated to what it normally measures. When this happens, quite pointedly, we attribute responsibility NOT to the circuit, NOT to the measurement, but to the "random chance".
So whenever such noise is louder than all the signals, it's the noise that steals causal focus from the system.
This means that whenever such locally
statistically independent data were to overcome the signal, this is is a constraint to free will, not a provider of it.
This is in fact one of the most important differences between the paradigm of compatibilism and radical fatalism: that inversion of the role of "randomness". You literally blame the noise and whatever is allowing it to be noisier than the signal.
(And there is where the radical fatalist really does get to blame something else such as the big bang for what happens, because the big bang created a lot of "noise" that only correlates to weird stuff happening far away).
Our goal is to keep stuff like the noise of the big bang as far away from how our minds function as is possible, according to compatibilists.