In Haym Soloveitchik's seminal essay "Rupture and Reconstruction" (1994) he lays out the state of Orthodoxy in the 20th century. Primarily, how Orthodoxy changed in the 20th century in particular regarding reliance on books, rather than tradition, and what effect that has on how people practice.
He writes:
"Fundamentally, all the above — stringency, “maximum position compliance,” and the proliferation of complications and demands — simply reflect the essential change in the nature of religious performance that occurs in a text culture. Books cannot demonstrate conduct; they can only state its requirements. One then seeks to act in a way that meets those demands. Performance is no longer, as in a traditional society, replication of what one has seen, but implementation of what one knows. Seeking to mirror the norm, religious observance is subordinated to it. In a text culture, behavior becomes, inevitably, a function of the ideas it consciously seeks to realize."
I have sat in no shortage of halachic shiurim. In many different settings I have heard different versions of "maximum position compliance" essentially meaning that if there is more than one opinion we paskin according to the most stringent to 'comply with' the greatest number of positions.
Is the idea of "maximum position compliance" an unspoken consequence of the culture and circumstance of 20th century Jewry, as laid out in that essay? Often one reads that the lenient position can be used in a time of need or bediavad; I'm not asking about that.
I am looking for a source lays out this doctrine explicitly as a general rule i.e., something like "when there is more than one position, we take the machmir one".
Update: I had considered תפסת מרובה לא תפסת, תפסת מועט תפסת. However, the gemarot that refer to this seem to be talking about cases of doubt specifically (e.g., Rosh HaShana 4b, Yoma 80a).