Different English translations translate this verse (1 Thessalonians 1:4) as follows:
Knowing, brethren beloved, your election of God. (KJV)
knowing, beloved brethren, your election by God. (NKJV)
knowing your election, brothers loved by God. (HCSB)
knowing, brethren beloved by God, His choice of you; (NASB)
What is the most accurate translation? Who made the election? Election of what?
NOTE: I'm looking for an answer free of assumptions of theological systems.
The prepositional phrase ὑπὸ τοῦ θεου (hypo tou theou) immediately follows ἀδελφοὶ ἠγαπημένοι (adelphoi ēgapēmenoi), and so the most natural reading (and that followed by virtually all modern translations) is "brothers beloved by God" (in fact I am not aware of any translations outside of the N/KJV that translate it any other way). "The election" is followed by a genitive possessive pronoun (τὴν ἐκλογὴν ὑμῶν, tēn eklogēn hymōn), i.e. "the election of you", best translated simply as "your election". The KJV (and NKJV, which is more or less an attempt to modernize the English used in the KJV) likely translated the passage the way they did in order to emphasize that "your election" is of God (the 1611 edition of the KJV even has a footnote in the margin indicating the "alternate" reading1), but this is not how the Greek actually reads. The Greek text itself simply says "your election".
With that said, election is always "God's choice" in Pauline writings:
"The election of you," that is, "that you have been chosen," namely, by God, as always in Paul. The eternal choice of God, "the divine purpose which has worked on the principle of selection"..., includes, according to II [Thessalonians] 2:14, not only the salvation of the readers but also the means by which or the state in which salvation is realized.
The words ἐκλέγεσθα (1 Cor. 1:27 ff. Eph. 1:4), ἐκλεκτό (Rom. 16:33) [sic], ἐκλεκτοὶ θεου (Rom. 8:33, Col. 3:12), and ἐκλογη (Rom. 9:11, 11:5, 7, 28) are rare in Paul. ἐκλογη does not occur in the LXX.... κλῆσι (II [Thessalonians] 1:11), καλεῖ (2:12, 4:7, 5:24) is the historical calling mediated by the preaching of the gospel (II [Thessalonians] 2:14).2
Because of this, many modern translators clarify whose 'choice' ('election') it is, such as the ESV, NRSV, NIV, NET, and NASB (as shown in the question, but note that "His" is italicized in the NASB translation to indicate that this is not in the original Greek text).
The main difficulty in translating this passage has nothing to do with the prepositional phrase, but rather the adverbial (or circumstantial) participle εἰδότες (eidotes), which most of the cited translations have elected (pun intended) to simply render as "Knowing, ...", which is a perfectly acceptable translation. Adverbial participles are subordinate to their controlling verb.3 The adverbial participle occurs here in a long introductory clause wherein it modifies Εὐχαριστοῦμεν (Eucharistoumen), i.e. "We give thanks...." This entire clause (vv. 2-5) could be outlined as follows:
We give thanks to God always for all of you,
making mention of you in our prayers,
constantly bearing in mind
your work of faith
and labor of love
and endurance of hope
in our Lord Jesus Christ
in the presence of our God and Father,
knowing,
brothers beloved by God,
your election,
because our gospel did not come to you
in word only,
but also in power
and in the Holy Spirit
and with full conviction,
just as you know
what sort of people we proved to be
among you
for your sakes.
This entire clause is one sentence in the original Greek text (and arguably continues beyond v. 5). Due to the length and complexity of this sentence, some English translators opt to translate the participle (εἰδότες, eidotes) as a finite verb instead ("For we know, ..."), such as the NRSV and ESV.
"Knowing" (εἰδότες, eidotes) modifies "we give thanks" (Εὐχαριστοῦμεν, Eucharistoumen), telling the reader why thanks is given: the election of Paul's readers. Paul goes on to explain his confidence in his readers' election: "because" (ὅτι, hoti) the gospel he proclaimed came to his readers "in power and in the Holy Spirit and with full conviction" (and Paul continues this line of thought in v. 6).
1 The KJV 1611 footnote reads, "Or, beloved of God, your election".
2 James Everett Frame, A Critical and Exegetical Commentary on the Epistles of St. Paul to the Thessalonians, International Critical Commentary (New York: C. Scribner’s Sons, 1912), 78. Available for free on archive.org.
3 "The adverbial or circumstantial participle is grammatically subordinated to its controlling verb (usually the main verb of the clause). Like an ordinary adverb, the participle modifies the verb, answering the question, When? (temporal), How? (means, manner), Why? (purpose, cause), etc."
Daniel B. Wallace, Greek Grammar Beyond the Basics - Exegetical Syntax of the New Testament (Zondervan Publishing House and Galaxie Software, 1996), 622.
1 Thessalonians 1:4 - Stephanus Textus Receptus 1550
εἰδότες ἀδελφοὶ ἠγαπημένοι ὑπὸ θεοῦ τὴν ἐκλογὴν ὑμῶν
Knowing | brothers | beloved | by/of | God | the | election | of you
Knowing, brethren beloved, your election of God. (KJV)
Here we see in the King James that the First Three Words match to the Greek. Next it says "your election" the Greek does support this by saying "the election of you".
Next it says "of God" the Greek does support this.
Without knowing the Greek there is so possibility of misreading this verse into believing that the one doing the electing is so the person, and the one being elected is so God.
knowing, beloved brethren, your election by God. (NKJV)
Here we see in the New King James that the first word matches to the Greek. Next it says "beloved brethren" now in English the word "beloved" is so an adjective. So in English placing the adjective before the noun "brethren" is so sound sentence structure. However the Greek word for "beloved" is so a verb. So although the "brethren are loved" because it is so saying "beloved brethren". The perspective of being "loved by God" is so not as easily seen. Next it says "your election" the Greek does support this by saying "the election of you". Next it says "by God" the Greek does support this. Looking between the KJV and the NKJV we can see that they fixed possibility of misreading, clearly God is so doing the election as the Greek supports.
knowing your election, brothers loved by God. (HCSB)
Here the election is what is "knowing" which the Greek does support because the verb "knowing" is so in the Nominative Case, and the "Election" is so in the Accusative Case meaning it is so the Subject that the Nominatives Apply to. We see that it does point out "your election" which is so correct. And also "Brother loved by God". However missing is so the doing the election of. This translation does not show that "being loved by God" does the election.
knowing, brethren beloved by God, His choice of you; (NASB)
Here we see all "knowing, brethren beloved by God" as directly in relation to the Greek. And also answers the questions "Who does the election?" and "Who is being elected?". However being elected has been simplified to a choice. Which does have a feel of a bit of a removal of the honor we really are given. The [meaning] to the word (ἐκλογὴν) is so "divine selection". So as "choice" does satisfy the textual need I do wish they could have added or kept the value.
Which is so the Most Correct?
From a position of saying which translation "more correctly" defines what the Greek is so trying to say. From the choices that have been given it is so the (NASB).
Who is so being Elected?
The Brethern that are so loved by God.
Who made the Election?
God is so the one who divinely selects.
Election of What?
Into God's divine selection.
