What you are describing is double-predestination - which is not what I believe the Bible teaches. Again, God forces nobody to go to Hell. And the "fairness" doctrine I hear so much about isn't really what people want. People don't want God to be fair because fair is sending ALL to Hell. Fair is not having His Son pay our penalty.
Romans 9 says that God basically "puts up with" objects that are fit for destruction in order to illustrate to those objects fit for His grace what His grace is all about. He allows those people THEIR own choice. I reject the concept of free will however for the lost because they are bound by sin. But, it's their desire to be against God. So, rather than telling people "YOU'RE NOT ALLOWED TO COME" God, recognizing that NOBODY would come on their own, chooses to save some while allowing the others their own inclinations. Again, He'd be fair to send ALL to Hell and isn't obligated to save anyone. Mercy and grace are what God exhibits when saving the individuals who will be saved.
Assuming I understand the terms, I don't see how you can have single predestination without double.
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.
That is my understanding of double predestination, which I happen to believe in. We are all lost, God chooses to save some. All those He chooses, He graces, and then all of them later choose Him. All those He passes over with this special grace are left to their own devices. All of them are lost.