Your code, and the other answers, are all buggy. They are missing the super() calls in the first two classes that are required for co-operative subclassing to work.
Here is a fixed version of the code:
class First(object):
def __init__(self):
super(First, self).__init__()
print("first")
class Second(object):
def __init__(self):
super(Second, self).__init__()
print("second")
class Third(First, Second):
def __init__(self):
super(Third, self).__init__()
print("third")
The super() call finds the next method in the MRO at each step, which is why First and Second have to have it too, otherwise execution stops at the end of Second.__init__().
This is what I get:
>>> Third()
second
first
third