Using a comparator function to sort

You're passing the comparator as the key function. You should be passing it as the cmp, wrapped in some kind of function that turns it into a proper comparator.

def make_comparator(less_than):
    def compare(x, y):
        if less_than(x, y):
            return -1
        elif less_than(y, x):
            return 1
        else:
            return 0
    return compare

sortedDict = sorted(subjects, cmp=make_comparator(cmpValue), reverse=True)

(Although actually, you should be using key functions:

sorted(subjects, operator.itemgetter(0), reverse=True)

Also note that sortedDict will not actually be a dict, so the name is rather confusing.)

In Python 3 there is no cmp argument for the sorted function (nor for list.sort).

According to the docs, the signature is now sorted(iterable, *, key=None, reverse=False), so you have to use a key function to do a custom sort. The docs suggest:

Use functools.cmp_to_key() to convert an old-style cmp function to a key function.

Here's an example:

>>> def compare(x, y):
...     return x[0] - y[0]
... 
>>> data = [(4, None), (3, None), (2, None), (1, None)]
>>> from functools import cmp_to_key
>>> sorted(data, key=cmp_to_key(compare))
[(1, None), (2, None), (3, None), (4, None)]

However, your function doesn't conform to the old cmp function protocol either, since it returns True or False. For your specific situation you can do:

>>> your_key = cmp_to_key(make_comparator(cmpValue))
>>> sorted(data, key=your_key)
[(1, None), (2, None), (3, None), (4, None)]

using the make_comparator function from @Fred Foo's answer.

The answer of @kaya3 is correct. I just propose another implementation in which we can use boolean for the comparator.

class YourTupleComparator(tuple):
    def __lt__(self, other):
        return self[0] < other[0]

sorted(subjects, key=YourTupleComparator)