Okay, I will give the best answer I can however, I suspect you are asking just to be argumentative. I pray not.
First you said:
It is true that God has chosen His elect before the foundation of the world. Tell me, what criteria has He based his choice on, seeing that it is not based on anything we have or can do in the way of good works, and that God is no respecter of persons. And if there is none righteous, no not one, as Romans says, then on what basis does God decide who is to be saved and who is to go to hell?
This is really a foolish question. Believers can only know what has been revealed by God in Holy Scripture. Holy Scripture does not reveal all of the mind of God. We see in Scripture - a hemisphere of God's revelation of the whole sphere. An entire hemisphere is hidden from our view. That portion of God's purpose, is none of our business. It is the area, that Scripture says, Even the Angels fear to tread. But the simple answer would be this:
Ps 115:1 Not unto us, O LORD, not unto us, but unto thy name give glory, for thy mercy, and for thy truth's sake.
Ps 115:2 Wherefore should the heathen say, Where is now their God?
Ps 115:3 But our God is in the heavens: he hath done whatsoever he hath pleased.
Ps 135:6 Whatsoever the LORD pleased, that did he in heaven, and in earth, in the seas, and all deep places.
Isa_44:24a Thus is saying Jehovah, thy Redeemer, and he that formed thee from the womb: I am Jehovah, that makes all things;...
Why would any true believer question what God can or cannot do. I love the fact that God does as He pleases. If He had desired to send me into condemnation - then so be it. I deserve it as a fallen creature. His Mercy, is what I do not deserve.
You also said:
As I asked in my previous post, please explain the contradiction between God choosing who is saved and who is to perish by His own decree, and yet every person is to be judged on their own choice of believing or rejecting the Gospel. How can a person be judged and condemned at the judgement if they had no choice in whether to be saved or not? Wouldn't a reprobate person have a defence at the judgement and say that he can't be condemned because God had already made the choice for him?
Herein, you seem to have a misunderstanding of what one is Judged for. The unsaved person will be judged because he/she is "dead in trespasses and sin" When Adam fell, he stood as our Federal Head before God and we all fell in him.
Rom 5:12 Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:
Ps 58:3 The wicked are estranged from the womb: they go astray as soon as they be born, speaking lies.
This brought about the curse of God upon fallen, sinful mankind. God's Holy nature sentence all of humanity to death. His Holy moral standard, (The ten commandments), proves we all deserve death. God's Holy Eternal Justice must be satisfied.
Thankfully, God had planned before the foundation of the world to save a remnant for Himself.
Heb_13:20 Now the God of peace, who brought again from the dead the great shepherd of the sheep with the blood of an eternal covenant, even our Lord Jesus,
Again there is no way of knowing how God chose whom He chose. Every human being is equally guilty. NONE stands higher than another. However, we can come to some conclusions. First and foremost God is the "Potter" and we are just clay in the Potters hands.
Isa_29:16 Ye turn things upside down! Shall the potter be esteemed as clay; that the thing made should say of him that made it, He made me not; or the thing formed say of him that formed it, He hath no understanding?
Isa_64:8 But now, O Jehovah, thou art our Father; we are the clay, and thou our potter; and we all are the work of thy hand.
Rom_9:21 Or hath not the potter a right over the clay, from the same lump to make one part a vessel unto honor, and another unto dishonor?
Paul asked the question for us: "Or hath not the potter a right over the clay? The answer: YES !! He is God and we are a mere created beings.
Christ satisfied God's Holy Justice as it could only be satisfied. He established a Righteousness for the Elect that Justified them before God. His Justifying work was ONLY for the Elect. The ones written in the Lamb's Book of Life before the foundation of the World. He died for the SHEEP (John 10:11, 15), not for the whole world. It is ridiculous to think that God would send His Son to die for the whole world, when He knows exactly the ones He intends to save. The word Cosmos in the Greek, is often used to mean: 1) a distinct group of people. 2) all of creation. 3) the earth 4) an operational system of mankind.
Now to your question about "contradiction".
There is no contradiction. Having established that all are equally GUILTY. Then how do we understand it? The Scripture says to us the following:
First, God will have MERCY and COMPASSION upon whom He will. The whom He will are the Elect. Rom 9:14-15 What shall we say then? Is there unrighteousness with God? God forbid. For he is saying to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion. He says again: Rom 9:18 Therefore hath he mercy on whom he will have mercy, and whom he will he hardens.
Your very question was anticipated by Paul: Rom 9:19-20 Thou wilt say then unto me, Why doth he yet find fault? For who hath resisted his will? Nay but, O man, who art thou that is speaking against God? Shall the thing formed say to him that formed it, Why hast thou made me thus?
What we know is, God chose some in Christ before the foundation of the world. He therefore, "passed by" all of the others. God does not increase the GUILT of the ONES He chose not to Elect to Salvation, they do that on their own. Their darkened, sinful nature will not come to the light to be saved, so they continue in their sin. Their "will" bound by sin and the fear of death. It would be same for the Elect, if God had not provided a new birth, (new nature), and a Righteous covering for them in Christ Jesus.
God choosing not to save any outside of the "Covenant of Redemption" harms no one, the lost continue upon the course they have always been on. A path that will ultimately place them in Eternal Condemnation and Punishment. There is a parallel to this kind of "mercy" being shown, even in our world. In Scripture, Pontius Pilate commuted the sentence of one man every year. We don't know why he would pick one over another but one was blessed with mercy and the other continued in prison. Pilate, not picking the other man in prison does no harm to him - as he was already guilty and in prison. The President of the United States has even greater powers given unto him. He can show mercy upon as many as he would like. Throughout American history, the President has released many from their judicial sentences. He does not have to give anyone a reason why or whom he picks for this mercy. It simply pleased him to do so.
I hope that answers your question.