Here is a good post that looks at some of the major difficulties in Calvinist accounting of free will and choice (below), It also does a good job concisely pointing out how Irresistible Grace is indeed coercive, even on some Calvinist definitions:
Excerpt:
The Coercion Problem
First, the Sproul-Edwards account of choice implies that God’s giving irresistible grace to the elect is coercive. To be sure, Sproul does say that it is a “misconception of irresistible grace” (122) to think it involves people being coerced “kicking and screaming against their wills.” Rather, they desire Christ because God “plants a desire for Christ” (123) in them.
Unfortunately, that’s not Sproul’s definition of ‘coercion’. For him, coercion involves “imposing choices upon people that, if left to themselves, they would not choose” (57). And in fact God does that to the elect. For God imposes an irresistible desire on the elect (for Christ), and as Sproul says “our choices are determined by our desires” (54). Therefore, God imposes choices on the elect by imposing irresistible desires on them. Moreover, these choices are ones they wouldn’t otherwise have made, since apart from irresistible grace no one can choose Christ.
So both the elect and non-elect are coerced in their “decisions.” And if we know anything at all about free choices, it’s this: they’re not coerced. Caused, perhaps; but a free coerced choice is a contradiction in terms.
Related:
Edwards’ Doctrine of Necessity by Strongest Motive Force Cannot be Proved
The Necessitarian Calvinist Argument From Strongest Motive Force is Based on Circular Reasoning
Thomas Ralston on Freedom of the Will Part 9: The Doctrine of Motives
The Reality of Choice and the Testimony of Scripture
The Fallacies of Calvinist Apologetics – Fallacy #5: Choices Apart From Intent?
Arminian Perspectives 
In the hard-deterministic flavour of Calvinism – your choice is not real, in the soft-deterministic flavour – your choice doesn’t matter.
And there you have it, right from the horse’s mouth. On a related topic, William Birch has a post that should be coming out soon on SEA’s website on compatibilism and free will. It’s originally found here: http://jacobarminius.blogspot.com/2015/01/compatibilism-vs-free-will.html?m=1
No matter how you look at it, every predestined action, word, thought or desire is inevitable in Calvinism–be it holy or evil–otherwise a Calvinist definition of sovereignty falls apart.
Richard,
I get what you are saying, but I personally think you are being too kind. I would say that even in compatibilism choice is not real. A hard determinist would just be honest enough to say that a determined choice is no choice at all. A compatibilist wants to have their cake and eat it too, but I am not “willing” to let them 🙂
Thanks Kangaroodort – unfortunately there is no ‘like’ or ‘upvote’ button.
Yes, I was being generous to the compatabilitst. By ‘choice’ in the compatabilist’s view of reality I am, of course, referring to their illusion of the ‘experience’ of choice.
We all know that by definition, a choice requires the actual and real possibility of choosing other than you did. The compatabilist attempts to redefince ‘choice’ as something more akin to ‘desire’. Two related but importantly distinct concepts.
To whom it may concern. Is there anyone who can show me on verse in the Bile that says that man prior to regeneration, (man in his natural state), has the power or the ability to choose Christ. Thank you kindly.
Neal,
No Arminian believes that man “in his natural state “has the ability to choose Christ. That’s why we need His enabling prevenient grace in order to believe. If you really want to educate yourself on what Arminians believe and why, here is a great place to start:
http://evangelicalarminians.org/the-facts-of-salvation-a-summary-of-arminian-theologythe-biblical-doctrines-of-grace/
You might be surprised by what you find.
Here is how James Arminius described man in his “natural state,”
“In this [depraved] state, the free will of man towards the true good is not only wounded, maimed, infirm, bent, and weakened; but imprisoned, destroyed, and lost. And its powers are not only debilitated and useless unless they are excited by Divine grace, but it has no powers whatever except such as are excited by Divine grace. For Christ has said, “Without me ye can do nothing”…..The mind of man, in this [depraved] state, is dark, destitute of the saving knowledge of God, and, according to the Apostle, incapable of those things which belong to the Spirit of God (1 Cor. 2:14),…” (From “Public Disputation” in Arminius Speaks, pp. 3, 4, brackets mine).
Here are two other good articles to help you clear up some common confusion among Calvinists about Arminianism:
https://arminianperspectives.wordpress.com/2011/04/23/nelson%E2%80%99s-dictionary-of-christianity-gets-it-wrong-examining-the-so-called-%E2%80%9C15-major-tenets-of-arminianism%E2%80%9D/
http://evangelicalarminians.org/survey-are-you-an-arminian-and-dont-even-know-it-2/