Rather than say that different people’s genealogies are being traced from the beginning, some prefer to stick with the most apparent meaning of the texts: that both lines do in fact go through Joseph. Counter to the linguistic concerns of the first argument, proponents of this second view would understand that Joseph is most likely the grammatical focus of both passages. To logically hold this view, one must explain the different names.
One subset of this theory is that the names of both genealogies refer to the same people under different names. As stated in the article about names, many people of this culture had several names. Perhaps one of the writers found a legal documentation of the line of Joseph while the other found the family tradition. Several names do appear to be similar. The legal names may represent family heads and would have to skip two or three generations on occasion.
A second subset could argue that all the names should belong to one single line with some or no names overlapping. Matthew already doctors his generational number, so he could just pick and choose whom to include. Luke feels free to add names from the Greek manuscripts, so he may also have variation on his part. It would be impossible to determine who was who’s son exactly since the line would be so out of order. Joseph’s own father would be either Heli or Jacob.
The third, and most common argument about the Joseph resolution goes back to the same issue in the first solution about legal verses literal lines. Luke may portray the physical lineage of Joseph while Matthew shows the legal inheritance line (often blood relation, but not necessarily. The Legal vs. family name option coincides with this). Joseph may or may not be an actual son of the kings, but has the technical right to the throne through Nathan. Matthew’s term “begat” is just the language of genealogy, and does not have to imply biological imparting (although this argument trends against the focus of the seed promise). This legal heir version of sonship may not have been uncommon in rabbinic thought. Because of this, the Christians of the time would have had no problem with the legality of Jesus’ right to the throne (since it did pass from David either way).
The second name set between Zerubbabal and David may be answered in similar terms as the above. The names that Luke provides may be the birth name of the kings and their actual sons, while Matthew uses the king title. There are more generations to fit into Luke’s time frame. One would have to recognize short generations between kings to keep the years congruent. Otherwise, it may be the same resolution as before: that Neri was a blood father, and Jeconiah was legal family head. The family title passes through Neri and his son.
The strengths and weaknesses of the above theory versions are as follows. The strength of the same persons theory is that both Matthew and Luke can provide factual content at apparent value without really having to stretch anything. The weakness is that the generations don’t line up, and it makes it difficult to synchronize how this actually would play out. It would make the authors pick and choose data at random without stated reason. Similar strengths (though not as strong) applies to the second theory. Little other advantages can be found to this solution. The greatest weakness for all is practicality. For that many generations to fit into one line would either push back the accepted time table of Israelite history, or cram all generations to an average of under twenty years. It also leaves the question of why the authors chose to do it that way and (intentionally?) avoid each other’s material.
The weakness of the last Joseph view is once again assumptions, as well as the context of Luke. The same assumptions about the first solution must be made about this second view (assumptions about who’s father is whom, the specific intention of the authors, and cultural standards). Additionally, Luke’s context, though focused on sonship, is not placed on Joseph, but on Jesus. There would be a major question why Luke would introduce Joseph’s bloodline when Jesus’ sonship is in question. This last version of the Joseph solution is the most common and is the strongest of the Joseph solutions. It makes the conflict of names disappear, and allows for Luke to trace the “exact truth” and for Matthew to trace “the King.”