Calvinism is the notion that our salvation – and even our very ability to “choose” good or have faith in God or believe in God is actually predetermined by God.

16 You did not choose me, but I chose you and appointed you so that you might go and bear fruit—fruit that will last—and so that whatever you ask in my name the Father will give you.

If Jesus means the apostles were unable to choose him, but instead he chose them, then this would indicate (Jesus) called people who would otherwise not have believed in him. This is reasonable support for Calvinism, although it should be noted that just because Jesus asked them to be disciples (would you be fishers of men?) does not mean they did not have the free will to reject him.

8 For by grace you have been saved through faith. And this is not your own doing; it is the gift of God,

9 not a result of works, so that no one may boast.

The reason why this is ambiguous is because the grace comes once you have faith; it is the claiming of faith which brings grace – although, many Calvinists will conflate the order of events here to state that faith and grace are co-equal, this is not a clear reading of the passage.

It seems there is greater support for “free-will” against Calvinism:

7 When a man's ways please the Lord, he makes even his enemies to be at peace with him.

This indicates that a man's ways may or may not please the Lord, and the Lord will take action based on his ways.

9 The heart of man plans his way, but the Lord establishes his steps.

This verse is clear in stating that it is man's choice in the matter to plan his way, although it is the Lord who will have the final say in how things play out.

3 Let not steadfast love and faithfulness forsake you; bind them around your neck; write them on the tablet of your heart.

4 So you will find favor and good success[a] in the sight of God and man.

5 Trust in the Lord with all your heart, and do not lean on your own understanding.

6 In all your ways acknowledge him, and he will make straight your paths.

These verses set the tone for the rest of Proverbs as well, as general advice. “If you do this, (then) God will find favor and good success in the sight of (God).” This does not indicate that God will pre-choose his faithful first, it indicates there is something you must do to seek the Lord's favor.

11 “For this commandment that I command you today is not too hard for you, neither is it far off.

12 It is not in heaven, that you should say, ‘Who will ascend to heaven for us and bring it to us, that we may hear it and do it?’

13 Neither is it beyond the sea, that you should say, ‘Who will go over the sea for us and bring it to us, that we may hear it and do it?’

14 But the word is very near you. It is in your mouth and in your heart, so that you can do it.

This passage is clear; the fulfilment of the law is not something God will bring down to you. Rather it is near to you that you may do it.

15 “See, I have set before you today life and good, death and evil.

16 If you obey the commandments of the Lord your God[a] …

17 But if your heart turns away, …

Here the Lord makes it clear that he has given us a chocice which we must act upon, and the result is not predetermined but rather “if, and if”.

This is driven home again and explicitly in v.19:

19 I call heaven and earth to witness against you today, that I have set before you life and death, blessing and curse. Therefore choose life, that you and your offspring may live,

God has called the universe to witness to the fact that the nation of Israel was given a choice.

<blockqoute>26 “See, I am setting before you today a blessing and a curse:

27 the blessing, if you obey…

28 and the curse, if you do not obey…</blockqoute>

Again it is indicated, directly by the Lord, that they have a choice to follow him or not.

24 A person’s steps are directed by the Lord. How then can anyone understand their own way?

Given the context of Proverbs, this doesn't necessarily mean that people do not have choice, as this is an echo of Proverbs 69.