I suppose many people get hung up at the doctrine of election and doctrine of approbation. A case in point is King Pharaoh, where God in Exodus chapter 7 verses 1 - 3, which reads
1 And the LORD said unto Moses, See, I have made thee a god to Pharaoh: and Aaron thy brother shall be thy prophet. 2 Thou shalt speak all that I command thee: and Aaron thy brother shall speak unto Pharaoh, that he send the children of Israel out of his land. 3 And I will harden Pharaoh's heart, and multiply my signs and my wonders in the land of Egypt.
Look at verse 3, where God said that He will harden Pharaoh's heart. The first mention of when Pharoah's heart will be hardened is in Exodus 4 verse 21 where God says that
When thou goest to return into Egypt, see that thou do all those wonders before Pharaoh, which I have put in thine hand: but I will harden his heart, that he shall not let the people go..
So God takes full responsibility for hardening Pharaoh's heart. If you study the 10 plagues, and the narrative that surrounds them,there was a combination of God hardening Pharaoh's heart and Pharaoh hardening his own heart. Romans chapter 9 sheds some more light on this issue. I will quote from verses 14 - 23. It reads
14 What shall we say then? Is there unrighteousness with God? God forbid.
15 For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion.
16 So then it is not of him that willeth, nor of him that runneth, but of God that sheweth mercy.
17 For the scripture saith unto Pharaoh, Even for this same purpose have I raised thee up, that I might shew my power in thee, and that my name might be declared throughout all the earth.
18 Therefore hath he mercy on whom he will have mercy, and whom he will he hardeneth.
19 Thou wilt say then unto me, Why doth he yet find fault? For who hath resisted his will?
20 Nay but, O man, who art thou that repliest against God? Shall the thing formed say to him that formed it, Why hast thou made me thus?
21 Hath not the potter power over the clay, of the same lump to make one vessel unto honour, and another unto dishonour?
22 What if God, willing to shew his wrath, and to make his power known, endured with much longsuffering the vessels of wrath fitted to destruction:
23 And that he might make known the riches of his glory on the vessels of mercy, which he had afore prepared unto glory,
The first question Paul asks is that Is God unrighteous in what He had determined shall happen to Esau and Jacob? The answer of course is an emphatic NO. Then Paul quotes from Exodus chapter 33 verse 19 where God told Moses about the fact that it is His prerogative to have mercy and to take vengeance. Verse 16 is a great comfort to all genuine Christians, because it tells us what verses such as John 6:44; John 6:37 and John 6:65 inform us, that our salvation in it's entirety is a gift from God. God the Father determined whom He will elect, God the Son died on the cross for the elect and God the Holy Spirit applied the salvation to the souls of the elect. Verse 17 tells us why Pharaoh was created. This is very scary in a sense, but John Calvin explains how approbation works in these words which I quote from chapter 18 of his institutes of the Christian Religion
From the first chapter of Job we learn that
Satan appears in the presence of God to receive his orders, just as do the angels who obey
spontaneously. The manner and the end are different, but still the fact is, that he cannot
attempt anything without the will of God. But though afterwards his power to afflict the
saint seems to be only a bare permission, yet as the sentiment is true, “The Lord gave, and
the Lord has taken away; as it pleased the Lord, so it has been done,” we infer that God was
the author of that trial of which Satan and wicked robbers were merely the instruments.
Satan’s aim is to drive the saint to madness by despair. The Sabeans cruelly and wickedly
make a sudden incursion to rob another of his goods. Job acknowledges that he was deprived
of all his property, and brought to poverty, because such was the pleasure of God. Therefore,
whatever men or Satan himself devise, God holds the helm, and makes all their efforts
contribute to the execution of his Judgments. God wills that the perfidious Ahab should be
deceived; the devil offers his agency for that purpose, and is sent with a definite command
to be a lying spirit in the mouth of all the prophets (2 Kings 22:20). If the blinding and infatuation
of Ahab is a Judgment from God, the fiction of bare permission is at an end; for
it would be ridiculous for a judge only to permit, and not also to decree, what he wishes to
be done at the very time that he commits the execution of it to his ministers. The Jews purposed
to destroy Christ. Pilate and the soldiers indulged them in their fury; yet the disciples
confess in solemn prayer that all the wicked did nothing but what the hand and counsel of
God had decreed (Acts 4:28), just as Peter had previously said in his discourse, that Christ
was delivered to death by the determinate counsel and foreknowledge of God (Acts 2:23);
in other words, that God, to whom all things are known from the beginning, had determined
what the Jews had executed. He repeats the same thing elsewhere, “Those things, which God
before had showed by the mouth of all his prophets, that Christ should suffer, he has so
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fulfilled,” (Acts 4:18). Absalom incestuously defiling his father’s bed, perpetrates a detestable
crime. God, however, declares that it was his work; for the words are, “Thou midst it secretly,
but I will do this thing before all Israel, and before the sun.”87 The cruelties of the Chaldeans
in Judea are declared by Jeremiah to be the work of God. For which reason, Nebuchadnezzar
is called the servant of God. God frequently exclaims, that by his hiss, by the clang of his
trumpet, by his authority and command, the wicked are excited to war.
In verse 19, Paul asks the question that will be in the mind of every reprobate (myself included, before God mercifully saved me). I love how verses 20 - 23 answers the question. It tells us how God is sovereign, not the author of sin, causes things to happen and yet hold those who do them accountable for their sins.
NB Sincere apologies if the formatting is not the best