Breaking ties in Python sort

Use a key function to sorted() and return a tuple; values will be sorted lexicographically:

sorted(yourlst, key=lambda t: (abs(t[0] - t[1])), t[0]), reverse=True)

I'm using abs() here to calculate a difference, regardless of which of the two integers is larger.

For your sample input, the key produces (1, 5), (3, 4) and (1, 6); in reverse order that puts (1, 6) (for the (6, 7) tuple) before (1, 5) (corresponding with (5, 6)).

Demo:

>>> yourlst = [(5, 6), (4, 1), (6, 7)]
>>> sorted(yourlst, key=lambda t: (abs(t[0] - t[1]), t[0]), reverse=True)
[(4, 1), (6, 7), (5, 6)]