In the documentation section 3.4.1 Basic customization (url: http://docs.python.org/ref/customization.html) it states:

There are no reflected (swapped-argument) versions of these methods (to be used when the left argument does not support the operation but the right argument does); rather, __lt__() and __gt__() are each other's reflection, __le__() and __ge__() are each other's reflection, and __eq__() and __ne__() are their own reflection.

Surely that should be __lt__() and __ge__() are each other's reflection, and __le__() and __gt__(). I assume this is just a typo, but I haven't checked that Python itself gets it right.

No, the documentation is correct (as well as Python's
behaviour). For example, you have a left_five and right_five,
which are int like objects with value 5, and left_five is
missing a __lt__ method. If you do a left_five < right_five
comparison, you want right_five's __gt__ method called,
because right_five's __ge__ method would return True,
since their values are equal.