the tense of the verb in a subordinate clause

The Cambridge Grammar (CGEL:151-158) clearly explains the rules under which backshift is obligatory. In this example, the event reported lies in the past of both my utterance and Sarah's, and therefore I am free to backshift ("had majored") or not ("majored" or "has majored"). Simplicity favours the non-backshifted version.

One factor that would increase the likelihood of backshifting is if I do not believe Sarah (CGEL:157), though even then the non-backshifted version is acceptable:

Yesterday Sarah told me that he also majored in sociology - but she was lying.

In this case, however, I would prefer to say "had", and I would be most unlikely to say "has".