The explanation is right in front of your eyes.
Like the restaurant menu, and the people choosing for themselves what they will have for dinner.
The action - according to your own definition - was determined to happen precisely as it happens before the customers were born or the restaurant built.
That is not choice. That is action proceeding as determined, not willed or chosen. The will to go to the restaurant is determined, the selection is determined, the meal arrives and it consumed as determined, including every word of the discussion, every twitch, laugh, feeling of pleasure, etc......that is how determinism works. And why free will is clearly not compatible with determinism
''All of these events, including my choices, were causally necessary from any prior point in time. And they all proceeded without deviation from the Big Bang to this moment.'' - Marvin Edwards.
It's reasons why free will is incompatible with determinism is entailed in the nature of determinism, as explained.
They are only incompatible if you use definitions that make it incompatible. If you define free will as "the opposite of determinism" or you define determinism as "the opposite of free will", then they become incompatible.
Your own definition of determinism makes free will incompatible with free will, as described above.
All that is required to make them compatible is to use the sensible definition of free will and the sensible definition of determinism.
I agree with your definition of determinism. It's the compatibilist definition of free will that's flawed beyond recovery.
Free will is when someone chooses for themselves what they will do, while free of coercion and undue influence.
Determinism is the belief that every event is reliably caused by prior events.
If determinism is true, nobody chooses. All actions are determined and proceed as determined. There are no possible alternatives in any given instance. Events proceed without deviation.
If you could have done otherwise - which is not possible - you could claim that you have choice.
But of course, as specified in the given definition, there is no deviation. With no possible deviation, nobody chooses what they: their actions must necessarily proceed as determined, without deviation
That's determinism.
When a person decides what they will do according to their own goals and their own reasons, the choice is reliably caused by prior events. Determinism is satisfied.
The person 'decides' precisely what is determined that they would 'decide.' Every thought and deliberation in each and every instance in time being fixed by the prior state of the system, everything proceeding without deviation (the given definition), the no choice principle of determinism.
When a person decides what they will do according to their own goals and their own reasons, the choice is reliably caused by that person. Free will is satisfied.
Goals, reasons, thoughts, deliberations and actions are not chosen, they emerge and proceed as determined by prior states of the system, this state becomes that state and the next without alternate options or choices, determinism doesn't allow multiple realizable choices, everything is necessitated, not willed. Will itself is fixed by the prior state of the system.
What Does Deterministic System Mean?
''A deterministic system is a system in which a given initial state or condition will always produce the same results. There is no randomness or variation in the ways that inputs get delivered as outputs.''
Necessity;
Necessity is the idea that everything that has ever happened and ever will happen is necessary, and can not be otherwise. Necessity is often opposed to chance and contingency. In a necessary world there is no chance. Everything that happens is necessitated.
''The No Choice Principle implies that I cannot have a choice about anything that is an unavoidable consequence of something I have no control of.''