Elaborating a bit, if God creates men who cannot but choose to sin- bound by sin with no freedom of choice as you describe, gives them the freedom to choose, then...
They're pre-destined for damnation, however you slice it. I think this is what you call double predestination.
The question is who are they predestined by? God did not force man to sin. Man did that to himself. Adam truly did have a choice. He was the one man with free-will. The rest are bound by sin that is not imposed on them by God but imposed on them through their ancestry and their own selfish desires.
Therefore, God does predestine one to Hell. He allows the situation to continue unimpeded until His plan for this world is complete.
Nobody goes to Hell wanting Christ. Nobody goes to Heaven who doesn't. God predestines some for Heaven. The rest, He allows to go on their own way due to their own desires. Fair for all is Hell. Fair is not the cross. Grace is the salvation which He has provided to His elect.