Mk:3.11 "I baptize you with water for repentance, but he who is coming after me is mightier than I, whose sandals I am not worthy to carry; he will baptize you with the Holy Spirit and with fire. 3.12 His winnowing fork is in his hand, and he will clear his threshing floor and gather his wheat into the granary, but the chaff he will burn with unquenchable fire."
Lk:1.7And he preached, saying, "After me comes he who is mightier than I, the thong of whose sandals I am not worthy to stoop down and untie. 1.8I have baptized you with water; but he will baptize you with the Holy Spirit."
Jn:3.15 As the people were in expectation, and all men questioned in their hearts concerning John, whether perhaps he were the Christ, 3.16 John answered them all, "I baptize you with water; but he who is mightier than I is coming, the thong of whose sandals I am not worthy to untie; he will baptize you with the Holy Spirit and with fire. 3.17 His winnowing fork is in his hand, to clear his threshing floor, and to gather the wheat into his granary, but the chaff he will burn with unquenchable fire." 3.18 So, with many other exhortations, he preached good news to the people.
In the case of Matthew and Mark, it is a simple case of them describing the baptism. John seems to intimately know the crowd's views, among them having been (Gnostic/Mandean?) supporters of John the Baptist. Luke seems to be at a distance, intellectually analyzing the situation as if a detective, saying that some thought he was the Messiah but unlike John does not directly quote them. Thus it is quite possible that Luke comes after John, and is in fact responding to John which is why he specifies "many" implying a great multitude of narratives, many of which are probably lost, many probably including the Gnostic Gospels/Nag Hammadi texts. He seems to be "fact checking" John, not necessarily because John is wrong but perhaps he suspects John is too close to the crowd being led astray (by Gnostics/Simon Magus/John the Baptist worshippers?), attempting to clarify things which may have resulted from misconceptions of John. For example, John's intimacy with this crowd may explain the similarities in themes that differ him from the synoptic gospels and place him closer to the tradition of Merkava Mysticism and Paul. (We can detect later possible influences of this community in Proto-Islam vis-a-vis the "Muhammad-Ali" duality.)1.24 Now they had been sent from the Pharisees. 1.25 They asked him, "Then why are you baptizing, if you are neither the Christ, nor Elijah, nor the prophet?" 1.26 John answered them, "I baptize with water; but among you stands one whom you do not know, 1.27 even he who comes after me, the thong of whose sandal I am not worthy to untie." 1.28 This took place in Bethany beyond the Jordan, where John was baptizing.
I have highlighted in bold face the common themes between the four gospels. These are:
- (1) After me comes who is mightier than me
- (2) Whose shoes I am not worthy to untie
- (3) I baptize with water
- (4) but he baptizes by the Holy Spirit
Matthew: (1) -- (2) -- (3) -- (4)
Mark: (1) -- (2) -- (4)
Luke: (3) -- (1) -- (2) -- (4)
John: (3) -- (1) -- (2)
In three out of the four cases, (2) appears before (4), and in all four cases, (1) appears before (2). The problematic element, however, is (3) which is absent in Mark and precedes all the other elements in Luke and John. Mark is known to miss things which are found in Matthew such as establishing a Jewish legitimacy for Jesus though that are also found in Luke, and since this fits the pattern if we establish Matthean primacy then (3) came after (2) and this was ignored by Mark. Under Markan primacy, (3) was originally absent and was therefore inserted by John, and therefore by Luke. Thus, Luke used both Matthew and Mark, and responded to John.
Due to the explicitly Jewish nature of Jesus and his movement I favour Matthean primacy and in fact a very early origin for this narrative; it would be unlikely for a later anti-Semitic/Gentile and Gnostic-influence church to want to fabricate claims linking Jesus to the Old Testament heritage. It is also pretty clear that Matthew is situated within broader Messianic claims of Second Temple Judaism (for example, in the work of Daniel Boyarin).
What remains to be addressed, however, is why Luke and John would feel the need to emphasize that John the Baptist baptizes with water while it is downplayed in Matthew and absent in Mark. I believe this is due to the prevalence of baptism within first century Judaic and Gnostic sects (indeed, ritual immersion continues to this day in Judaism and also in Islam), and the need to grant greater legitimacy to Jesus's baptism being secondary to an ordinary baptism. Thus Luke and John are establishing a greater authority of Jesus from the Divine, as the believers are given direct baptism in the Holy Spirit (i.e. unlike the Gnostics/Mandeans).
Thus in conclusion, I believe that Matthew and Mark came first, then John, and finally Luke in response to certain misunderstandings which emerged as a result of John's gospel leaning heavily into mysticism.