In a different forum this author (somewhat flippantly) made this comment about the Parable of the Sower in Luke: “I think I could make a case that some features (e.g. the use of moisture in Lk 8:6 instead of a lengthy explanation of the sun scorching the seeds because of a lack of earth, and just a 'hundredfold' in Lk 8:8) suggest that here Luke is following a different source.”
My point was to do with the interpretation of what (At least, for most people who are familiar with the Synoptic Problem) are ‘obvious’ triple tradition passages, i.e. where Mark, Matthew and Luke are clearly all referring to the same thing (whether speech, an event, or anything else), and there are small differences that can reasonably be explained as being due simply to a particular author’s characteristic way of expressing himself.
For example, as suggested above, in the Parable of the Sower both Mark and Matthew provide a fairly detailed explanation (Mk 4:5-6 and Mt 13:5-6) as to why the seed on stony ground withered away, while in Luke we have just the simple statement at the end of Lk 8:6 that it “lacked moisture.” On the assumption of Markan priority (i.e. that Mark was written before either Matthew or Luke) then one possible explanation for this is that aLuke (the author of Luke) saw Mark (and possibly Matthew) and simply chose to remove what he considered to be unnecessary detail from his version of the parable, but another possible explanation is that aLuke knew a different source that included a shorter version of the text, and based his version on that. If so, then it is possible that aMatthew could have seen also this shorter version but for whatever reason preferred the longer version he saw in Mark. In a similar way Lk 8:8a appears to simply ‘shorten’ Mk 4:8 and Mt 13:8, and again here aLuke could possibly have seen this shorter text in a source other than Mark or Matthew.
Because these are minor changes then, assuming Markan priority, the most parsimonious explanation (because it does not require a non-synoptic source) is that aLuke simply ‘tidied up’ text he saw in Mark, and (depending on the assumed synoptic hypothesis) also in Matthew, and there are other places in the synoptic gospels where the same explanation appears most likely. There are also places where it is Matthew that has the shorter text, and not surprisingly here it is reasonable to assume that aMatthew simply ‘tidied up’ what he saw in Mark, while aLuke followed Mark whether he saw the shorter version in Matthew or not. For perhaps most people the most reasonable assumption is that where we see three closely similar versions of the same text that this is simply due to one author making minor changes to what he saw in either one or both of the other gospels, and that there is no reason to suggest an additional (non-synoptic) source as a way of explaining the differences.
However, what if you already believe, for other reasons, that there was a non-synoptic source? For example, many people believe that text common to Matthew and Luke but not present in Mark came from another source, and the most commonly hypothesized such source is one known as Q, in what is known as the Mark-Q hypothesis or 2DH (2 document hypothesis). If Q (or another 'second source' - SS) existed then it is possible that some text common to Matthew and Luke where there is also a parallel in Mark could also have come from Q/SS rather than Mark, or as in the example given above, aLuke could have obtained his slightly shorter Parable of the Sower from Q/SS, while aMatthew used the version he saw in Mark. On the Mark-Q hypothesis neither aMatthew nor aLuke used each other’s gospel, so on that hypothesis we could reasonably expect that they sometimes did not use the same source in places where Mark and Q had parallels, i.e. where they ‘overlapped,’ and the term ‘Mark-Q overlap’ is often used in this context.
Parallel text in Matthew and Luke where none exists in Mark is commonly referred to as being part of the Double Tradition, or as Double Tradition text. However, it should be noted that strictly speaking there are three ‘double traditions,’ because there are three possible combinations of parallel text in two of the synoptic gospels with none in the third, but Double Tradition (with capitals) is commonly used to refer specifically to the one in which Matthew and Luke contain the parallels. In contrast, there is only one Triple Tradition (parallels in all three synoptic gospels), but in both the Double Tradition and the Triple Tradition there is the question of how much difference between the gospels is allowed before a possible ‘Double Tradition’ or a ‘Triple Tradition’ passage is thought of as something else instead. For example, by most standards Mt 10:7-13 / Lk 10:4-9 is Double Tradition text because it has no parallel in Mark, even though the ordering of the text is not the same in Matthew and Luke, many of the words are different although the meaning is essentially the same, and Lk 10:7a has no parallel in Matthew and most of Mt 10:8 has no parallel in Luke. These are clearly strongly related pieces of text for which Mark has no parallel, but do their differences mean that it is unlikely for them to have had the same single source?
By definition the text of any hypothetical source (Q or otherwise) used by aMatthew and aLuke where Mark has no text is not predetermined. Consequently, it can be hypothesized to include as much or as little text parallel to Mark as is allowed in the assumed hypothesis, which in this case includes text where at first sight it would appear that aMatthew and/or aLuke are simply making minor changes to Mark, as for example in the Parable of the Sower. However, what is interesting here is that while most of the differences between Mk 4:1-9 and Mt 13:1-9 are quite trivial, on the assumption that Mark was seen by both aMatthew and aLuke, Lk 8:4-8 is not just shorter, but has other changes that seem to have no rationale, begging the question of why aLuke would bother making them. Having a different location at the beginning of a passage is quite common in synoptic parallels, but why in Lk 8:5 would aLuke add that the seed was trodden down? Yes, of course aLuke is ‘allowed’ to do this, but this and at least some of these changes could be regarded as aLuke here following a different source to either aMark or aMatthew, so that on the assumption of Markan priority this would be a Mark/Matthew - other source (SS etc.) overlap.
While the suggestion of a different form of overlap in the Parable of the Sower (e.g., not Mark-Q but Mark/Matthew-SS) may seem to be a stretch, there are other places where the possibility of a different overlap cannot be so easily dismissed, as for example in the call of the disciples. Here Mk 1:16-20 / Mt 4:18-22 are close parallels even though a few of the details are different, for example naming Simon as Peter in Mt 4:18 and referring to the servants in Mk 1:20. However, Lk 5:1-11 has almost nothing in common with Mk 1:16-20 / Mt 4:18-22 except the names of the participants, so that it is clear that aLuke has not simply added detail to what he saw in Mark and possibly Matthew, but instead that this is a completely different telling of Jesus calling his disciples to him. On the Mark without Q (MwQH) or Farrer hypothesis aLuke apparently rejected what he saw in both Mark and Matthew and instead either created his own much longer version or obtained it from one of his ‘many’ sources, while on the Mark-Q hypothesis he rejected just Mark (by definition he did not know Matthew) in favor of his own creation or another source. However, on the Mark-Q hypothesis Q already is that other source, so it makes no sense to suggest yet another source for Lk 5:1-11 when a possible one already exists in the hypothesis. Either Lk 5:1-11 was written by aLuke himself, or he saw at least a version of it in Q.
On the Mark-Q hypothesis having anything other than Q being the source of Lk 5:1-11 (including aLuke having written it himself) is ‘multiplying entities unnecessarily’ and so should not be considered, and the same principle applies to any hypothesis that assumes Markan priority and a second source that is not Q, e.g. a hypothesis in which Matthew and Luke are not required to be independent. Given that an additional source (Q or SS) is already assumed in such hypotheses, every passage in which Mark and Matthew agree significantly against Luke, and those in which Mark and Luke agree significantly against Matthew, should be evaluated as respectively being possible Mark/Matthew–Q/SS or Mark/Luke–Q/SS overlaps.
Of course, what is ‘significant’ to one person may be ‘not significant’ to another, but where a non-synoptic source for Matthew and Luke is already an integral part of a hypothesis that assumes Markan priority, any passage in Matthew and/or Luke that differs significantly from its parallel in Mark should be assumed to have originated in that non-synoptic source unless there is a specific reason to reject it, instead of assuming that it originated in Mark unless there is a specific reason to reject it as having been in that source. Essentially, where another source is already hypothesized for other reasons Mark should not be assumed to be the ‘default’ source where there are major differences that are hard to explain as simply authorial preference.