What is the Biblical Basis for saying that people determine for themselves whether they will be saved or not?

This is a loaded question assuming that there is a biblical basis for saying that people determine for themselves whether they will be saved or not. ;-)

I side with Ray Butterworth's answer that there is no biblical basis for anyone (but Jesus) going to God's Heaven.

PS. I think my 'answer' is more suited as a comment, but I don't have a high enough reputation to comment . . . sorry.

The simple answer is that there is no biblical basis for anyone (but Jesus) going to God's Heaven.

That idea is one of many non-biblical concepts that most Christians seem to accept without any biblical evidence.

For many decades, people have offered cash to anyone that can show where the Bible promises that the reward of the saved is to go to Heaven. No one has ever successfully claimed the offer.

Here are a couple of examples:

For over twenty-eight years, I have offered a certified cashier’s check for $10,000 to anyone who can come up with the words “immortal soul,” “When we get to heaven,” “I will see you in heaven,” and “We go to heaven when we die.”

Not in all those twenty-eight years, with millions hearing my words, has a single person been able to claim the certified cashier’s check for $10,000!

Why not?

Simply because such words are not in the Bible!

— Believe it or Not… The Bible Does NOT Promise “Heaven”! – Garner Ted Armstrong Evangelistic Association

and:

Do The Dead Go To Heaven?

Well, I wondered when I saw some of these passages; and I began to wonder what happens to a soul when it does die? "...the soul that sinneth, it shall die" (Ezekiel 18:4). And Adam sinned and Adam did die. He lived 930 years and he died. Now we don't like to use that term 'die' today, we like to say; "Well, so and so passed away." They were a soul, and the soul passed out of them and passed away somewhere. Well where did they pass? Do they see you today? Are they alive? Are they watching you? Do they know what you're doing? Well, notice what Jesus said. Now in the third chapter of the book of John, John the third chapter and in verse 13, and Jesus said:

"And no man hath ascended up to heaven, but he that came down from heaven, even the Son of man which is in heaven." (John 3:13)

Only Christ who came from heaven has ever ascended to heaven of all human men, all human beings on the earth. No man has ascended up to heaven. Now I want to take you through a few scriptures. How do you know? I didn't know at one time, and I began to see something in the scriptures that at that time I didn't agree with. And I began to find I was wrong, and I found God was right. And you know, I had to give up what I believed. And if you'll blow the dust off your Bible and look into your Bible awhile you'll begin to find the same thing.

Now you hear people talk about going to heaven; I heard a minister say on the air before millions of people; "The Bible says, 'when we all get to heaven'." I'll give that man a thousand dollars if he'll show me where the Bible says that, because it doesn't say anything of the kind. Not anywhere in your Bible - it teaches just the opposite. What does God say? Will you agree with God? Or do you think God is wrong, and all of the people are right?

— Not In Heaven - The World Tomorrow Radio Broadcast

On Stack Christianity, a specific question gets specific answers. You specifically asked "WHO decides whether I go to heaven?" not "WHAT decides whether I go to heaven?" Your specific question would get concentrated answers as to why God determines who gets into his heaven. After all, it's his dwelling place (Deuteronomy 26:15; Psalm 46:4; 1 Timothy 6:15-16)! There are unlikely to be many answerers here who would disagree with God being the one who ultimately determines whether you (or anyone else) gets into heaven. Granted, some denominations think a particular person who they say founded their group will be delegated that task, but the Bible is clear that it is only Jesus Christ who judges everyone (John 5:21-23).

However, you then immediately introduced that different question, as to WHAT determines entry, by providing the link for The Coastal Courier article about that. Then you referred us to the Quora page which goes all over the place with random answers and a whole raft of related questions. That page is all about peoples' opinions, and often descends into arguments between people with differing beliefs.

Stack Christianity actively discourages that kind of thing. Focused questions are encouraged, with laser-like answers sticking to the point. This means that your question at the top is clear, and so is the related one in your comments, "But if it's me who decides, why can't I just decide that I'll go to heaven regardless of whether I follow the gospel?"

My answer to those two connected questions is simply this: God has revealed to humanity in his written word what heaven is all about, and why it is not open to all people, after they have died. In particular, in the last book of the Bible, he has used pictorial language to point to a future day when all the living and all the dead will be judged before the great white throne, some being cast away, others allowed in (Revelation 21:11-15). There is far too much in the Bible about this to put into an answer here. Much of what Jesus said, while on earth, deals with the kingdom of heaven and who get in and who are kept out.

As the risen Christ is the judge before whom all will stand for judgment, and the gospel is the good news of Christ (what he did to open up heaven being one aspect of that), then to know WHAT is required by God and Christ to get into the kingdom of heaven would entail studying what the Bible says about all of that. But that, as I have pointed out, is another question! Grasping whether there's any link between that and human free will cannot begin until first God's authority and God's requirements are believed.

Once your first question is resolved, then the second question you raised is settled. No human decides for themself! The reason why believing and obeying the gospel of Christ is so vital follows on. Only then can the question of free will be tackled. But referring us to those other sites is just muddying the waters. Hopefully, other answers will go more deeply into God being the one who decides who gets into his heaven.