When I talk to people (average, ordinary people) they mean by choice just what Calvinism teaches about what choice is: people picking from among various options. They normally don't impose much of a philosophical framework on it.
If I ask them, "What if someone forces you to pick A?" They would reply that this isn't really a choice. Of course, that's because there's compulsion involved.
On the other hand, if I ask them how they got their now-spouse to pick them, they will have some kind of answer. Sometimes the answer is that they "just fell in love," sometimes the answer is persistence on the part of one of the two spouses, but ultimately the person normally acknowledges some causal relation at play, although they still view the relationship as a voluntary association.
I could go further with the nuances (such as the fact that people buy advertising because they think they can influence choices), but the bottom line is that generally speaking every "average Joe" I speak to has roughly the same answers to the questions about choice, and they all line up either exactly with what Calvinism teaches about choice, or awfully close.
On the other hand, when I talk to folks who are "Arminian theologians" (of greater or lesser sophistication), I generally find them appealing to philosophical definitions of choice that (a) don't matter to the common man, (b) aren't readily intelligible either to the Arminians themselves or the common man, and (c) don't come from Scripture.
Personally, I find (c) to be the most problematic of the matters. The truth is that Scriptures clearly teach that God has foreordained whatsoever comes to pass (see Acts 17:26, for example), that men make choices (see, for example, Isaiah 65:12), and that God has a purpose in evil the evil acts of men (see, for example, Genesis 50:20). These truths are compatible, whether people like it or not. Everything is part of God's plan, even our choices.
Proverbs 16:4 The LORD hath made all things for himself: yea, even the wicked for the day of evil.
This is the truth of Scripture. God has made all things for himself - even the wicked. He has a purpose in everything. That's why he sets up as a test of deity that an alleged god explain the reasons for history and tell the future. God can do those things because History is written by God:
21 Produce your cause, saith the LORD; bring forth your strong reasons, saith the King of Jacob. 22 Let them bring them forth, and shew us what shall happen: let them shew the former things, what they be, that we may consider them, and know the latter end of them; or declare us things for to come. 23 Shew the things that are to come hereafter, that we may know that ye are gods: yea, do good, or do evil, that we may be dismayed, and behold it together.
This is how great God is. He holds all of history in the palm of his hand - he turns kings hearts, whatever direction it pleases Him.
Proverbs 21:1 The king's heart is in the hand of the LORD, as the rivers of water: he turneth it whithersoever he will.
And if Kings' hearts are under God's control, don't think that God only has a thought for them, but not for the lesser details:
6 Are not five sparrows sold for two farthings, and not one of them is forgotten before God? 7 But even the very hairs of your head are all numbered. Fear not therefore: ye are of more value than many sparrows.
This is what the Bible has to say, and we need to believe it.
But I was surprised and disappointed to hear of a counter-argument attempted from those who embrace the philosophical position of Libertarian Free Will (LFW). They have attempted to claim that their position is what common men hold, despite the great evidence to the contrary. However, Mr. Manata, employing his usual rapier wit, has provided a brief rejoinder to one of their claims (link). While I certainly find his point amusing, I hope the positive presentation above briefly provides the reason that I think the shoe is really on the other foot. It is the Arminian concept of LFW that is foreign to the average Joe. The average Joe can readily see that choices have reasons and explanations that go beyond the mere whim of the person making the choice. While the average Joe may not fully comprehend how choice and universal predestination can co-exist, this is often because of caricatures of predestination (such as the fatalism caricature) that are provided.
But let me leave you, the reader, on a more interesting note. People talk about the fact that the word "choose" is in the Bible. But did you notice who that is usually talking about?
1. (Exodus 17:9) And Moses said unto Joshua, Choose us out men, and go out, fight with Amalek: to morrow I will stand on the top of the hill with the rod of God in mine hand.
2. (Deuteronomy 30:19) I call heaven and earth to record this day against you, that I have set before you life and death, blessing and cursing: therefore choose life, that both thou and thy seed may live:
3. (Joshua 24:15) And if it seem evil unto you to serve the LORD, choose you this day whom ye will serve; whether the gods which your fathers served that were on the other side of the flood, or the gods of the Amorites, in whose land ye dwell: but as for me and my house, we will serve the LORD.
4. (1 Samuel 17:8) And he stood and cried unto the armies of Israel, and said unto them, Why are ye come out to set your battle in array? am not I a Philistine, and ye servants to Saul? choose you a man for you, and let him come down to me.
5. (2 Samuel 17:1) Moreover Ahithophel said unto Absalom, Let me now choose out twelve thousand men, and I will arise and pursue after David this night:
6. (2 Samuel 24:12) Go and say unto David, Thus saith the LORD, I offer thee three things; choose thee one of them, that I may do it unto thee.
7. (1 Kings 18:23) Let them therefore give us two bullocks; and let them choose one bullock for themselves, and cut it in pieces, and lay it on wood, and put no fire under: and I will dress the other bullock, and lay it on wood, and put no fire under:
8. (1 Kings 18:25) And Elijah said unto the prophets of Baal, Choose you one bullock for yourselves, and dress it first; for ye are many; and call on the name of your gods, but put no fire under.
9. (1 Chronicles 21:10) Go and tell David, saying, Thus saith the LORD, I offer thee three things: choose thee one of them, that I may do it unto thee.
10. (1 Chronicles 21:11) So Gad came to David, and said unto him, Thus saith the LORD, Choose thee
11. (Nehemiah 9:7) Thou art the LORD the God, who didst choose Abram, and broughtest him forth out of Ur of the Chaldees, and gavest him the name of Abraham;
12. (Job 9:14) How much less shall I answer him, and choose out my words to reason with him?
13. (Job 34:4) Let us choose to us judgment: let us know among ourselves what is good.
14. (Job 34:33) Should it be according to thy mind? he will recompense it, whether thou refuse, or whether thou choose; and not I: therefore speak what thou knowest.
15. (Proverbs 1:29) For that they hated knowledge, and did not choose the fear of the LORD:
16. (Proverbs 3:31) Envy thou not the oppressor, and choose none of his ways.
17. (Isaiah 7:15) Butter and honey shall he eat, that he may know to refuse the evil, and choose the good.
18. (Isaiah 7:16) For before the child shall know to refuse the evil, and choose the good, the land that thou abhorrest shall be forsaken of both her kings.
19. (Isaiah 56:4) For thus saith the LORD unto the eunuchs that keep my sabbaths, and choose the things that please me, and take hold of my covenant;
20. (Isaiah 65:12) Therefore will I number you to the sword, and ye shall all bow down to the slaughter: because when I called, ye did not answer; when I spake, ye did not hear; but did evil before mine eyes, and did choose that wherein I delighted not.
21. (Ezekiel 21:19) Also, thou son of man, appoint thee two ways, that the sword of the king of Babylon may come: both twain shall come forth out of one land: and choose thou a place, choose it at the head of the way to the city.
22. (Philippians 1:22) But if I live in the flesh, this is the fruit of my labour: yet what I shall choose I wot not.
1. (Numbers 16:7) And put fire therein, and put incense in them before the LORD to morrow: and it shall be that the man whom the LORD doth choose, he shall be holy: ye take too much upon you, ye sons of Levi.
2. (Numbers 17:5) And it shall come to pass, that the man's rod, whom I shall choose, shall blossom: and I will make to cease from me the murmurings of the children of Israel, whereby they murmur against you.
3. (Deuteronomy 7:7) The LORD did not set his love upon you, nor choose you, because ye were more in number than any people; for ye were the fewest of all people:
4. (Deuteronomy 12:5) But unto the place which the LORD your God shall choose out of all your tribes to put his name there, even unto his habitation shall ye seek, and thither thou shalt come:
5. (Deuteronomy 12:11) Then there shall be a place which the LORD your God shall choose to cause his name to dwell there; thither shall ye bring all that I command you; your burnt offerings, and your sacrifices, your tithes, and the heave offering of your hand, and all your choice vows which ye vow unto the LORD:
6. (Deuteronomy 12:14) But in the place which the LORD shall choose in one of thy tribes, there thou shalt offer thy burnt offerings, and there thou shalt do all that I command thee.
7. (Deuteronomy 12:18) But thou must eat them before the LORD thy God in the place which the LORD thy God shall choose, thou, and thy son, and thy daughter, and thy manservant, and thy maidservant, and the Levite that is within thy gates: and thou shalt rejoice before the LORD thy God in all that thou puttest thine hands unto.
8. (Deuteronomy 12:26) Only thy holy things which thou hast, and thy vows, thou shalt take, and go unto the place which the LORD shall choose:
9. (Deuteronomy 14:23) And thou shalt eat before the LORD thy God, in the place which he shall choose to place his name there, the tithe of thy corn, of thy wine, and of thine oil, and the firstlings of thy herds and of thy flocks; that thou mayest learn to fear the LORD thy God always.
10. (Deuteronomy 14:24) And if the way be too long for thee, so that thou art not able to carry it; or if the place be too far from thee, which the LORD thy God shall choose to set his name there, when the LORD thy God hath blessed thee:
11. (Deuteronomy 14:25) Then shalt thou turn it into money, and bind up the money in thine hand, and shalt go unto the place which the LORD thy God shall choose:
12. (Deuteronomy 15:20) Thou shalt eat it before the LORD thy God year by year in the place which the LORD shall choose, thou and thy household.
13. (Deuteronomy 16:2) Thou shalt therefore sacrifice the passover unto the LORD thy God, of the flock and the herd, in the place which the LORD shall choose to place his name there.
14. (Deuteronomy 16:6) But at the place which the LORD thy God shall choose to place his name in, there thou shalt sacrifice the passover at even, at the going down of the sun, at the season that thou camest forth out of Egypt.
15. (Deuteronomy 16:7) And thou shalt roast and eat it in the place which the LORD thy God shall choose: and thou shalt turn in the morning, and go unto thy tents.
16. (Deuteronomy 16:15) Seven days shalt thou keep a solemn feast unto the LORD thy God in the place which the LORD shall choose: because the LORD thy God shall bless thee in all thine increase, and in all the works of thine hands, therefore thou shalt surely rejoice.
17. (Deuteronomy 16:16) Three times in a year shall all thy males appear before the LORD thy God in the place which he shall choose; in the feast of unleavened bread, and in the feast of weeks, and in the feast of tabernacles: and they shall not appear before the LORD empty:
18. (Deuteronomy 17:8) If there arise a matter too hard for thee in judgment, between blood and blood, between plea and plea, and between stroke and stroke, being matters of controversy within thy gates: then shalt thou arise, and get thee up into the place which the LORD thy God shall choose;
19. (Deuteronomy 17:10) And thou shalt do according to the sentence, which they of that place which the LORD shall choose shall shew thee; and thou shalt observe to do according to all that they inform thee:
20. (Deuteronomy 17:15) Thou shalt in any wise set him king over thee, whom the LORD thy God shall choose: one from among thy brethren shalt thou set king over thee: thou mayest not set a stranger over thee, which is not thy brother.
21. (Deuteronomy 18:6) And if a Levite come from any of thy gates out of all Israel, where he sojourned, and come with all the desire of his mind unto the place which the LORD shall choose;
22. (Deuteronomy 23:16) He shall dwell with thee, even among you, in that place which he shall choose in one of thy gates, where it liketh him best: thou shalt not oppress him.
23. (Deuteronomy 26:2) That thou shalt take of the first of all the fruit of the earth, which thou shalt bring of thy land that the LORD thy God giveth thee, and shalt put it in a basket, and shalt go unto the place which the LORD thy God shall choose to place his name there.
24. (Deuteronomy 31:11) When all Israel is come to appear before the LORD thy God in the place which he shall choose, thou shalt read this law before all Israel in their hearing.
25. (Joshua 9:27) And Joshua made them that day hewers of wood and drawers of water for the congregation, and for the altar of the LORD, even unto this day, in the place which he should choose.
26. (1 Samuel 2:28) And did I choose him out of all the tribes of Israel to be my priest, to offer upon mine altar, to burn incense, to wear an ephod before me? and did I give unto the house of thy father all the offerings made by fire of the children of Israel?
27. (2 Samuel 16:18) And Hushai said unto Absalom, Nay; but whom the LORD, and this people, and all the men of Israel, choose, his will I be, and with him will I abide.
28. (2 Samuel 21:6) Let seven men of his sons be delivered unto us, and we will hang them up unto the LORD in Gibeah of Saul, whom the LORD did choose. And the king said, I will give them.
29. (1 Kings 14:21) And Rehoboam the son of Solomon reigned in Judah. Rehoboam was forty and one years old when he began to reign, and he reigned seventeen years in Jerusalem, the city which the LORD did choose out of all the tribes of Israel, to put his name there. And his mother's name was Naamah an Ammonitess.
30. (Psalms 25:12) What man is he that feareth the LORD? him shall he teach in the way that he shall choose.
31. (Psalms 47:4) He shall choose our inheritance for us, the excellency of Jacob whom he loved. Selah.
32. (Isaiah 14:1) For the LORD will have mercy on Jacob, and will yet choose Israel, and set them in their own land: and the strangers shall be joined with them, and they shall cleave to the house of Jacob.
33. (Isaiah 49:7) Thus saith the LORD, the Redeemer of Israel, and his Holy One, to him whom man despiseth, to him whom the nation abhorreth, to a servant of rulers, Kings shall see and arise, princes also shall worship, because of the LORD that is faithful, and the Holy One of Israel, and he shall choose thee.
34. (Isaiah 66:4) I also will choose their delusions, and will bring their fears upon them; because when I called, none did answer; when I spake, they did not hear: but they did evil before mine eyes, and chose that in which I delighted not.
35. (Zechariah 1:17) Cry yet, saying, Thus saith the LORD of hosts; My cities through prosperity shall yet be spread abroad; and the LORD shall yet comfort Zion, and shall yet choose Jerusalem.
36. (Zechariah 2:12) And the LORD shall inherit Judah his portion in the holy land, and shall choose Jerusalem again.
I know that this is just statistical data, but there is an emphasis in Scripture. The emphasis in Scripture is on the works of God. The central focal point of the Scripture is the Gospel of Christ, the glad tidings of the sacrifice that He has made for the redemption of his people. It is by Christ's death that sin has been conquered: that was God's choice, not ours. And even though men chose to crucify God, this too was ordained by God:
22 Ye men of Israel, hear these words; Jesus of Nazareth, a man approved of God among you by miracles and wonders and signs, which God did by him in the midst of you, as ye yourselves also know: 23 Him, being delivered by the determinate counsel and foreknowledge of God, ye have taken, and by wicked hands have crucified and slain: 24 Whom God hath raised up, having loosed the pains of death: because it was not possible that he should be holden of it.
Praise be to God!