TypeError: 'cmp' is an invalid keyword argument for this function

You should try to rewrite your cmp function to a key function instead. In this case it looks like you can simply return the counter() function output for just one element:

def my_key(elem):
    counter = lambda x, items: sum(list(x).count(xx) for xx in items)
    return counter(elem, [2, 3, 4, 5]), len(elem)

I took the liberty of replacing the reduce(...) code with the sum() function, a far more compact and readable method to sum a series of integers.

The above too will first sort by the output of counter(), and by the length of each sorted element in case of a tie.

The counter function is hugely inefficient however; I'd use a Counter() class here instead:

from collections import Counter

def my_key(elem):
    counter = lambda x, items: sum(Counter(i for i in x if i in items).values())
    return counter(elem, {2, 3, 4, 5}), len(elem)

This function will work in both Python 2 and 3:

sorted(zip(tracks, self.mapping[idx][track_selection[-1]].iloc[0]),
       key=lambda x: my_key(x[1]))

If you cannot, you can use the cmp_to_key() utility function to adapt your cmp argument, but take into account this is not an ideal solution (it affects performance).

from python documentation

In Python 2.7, the functools.cmp_to_key() function was added to the functools module.

The function available in python 3 too.

Just wrap your cmp function with cmp_to_key

from functools import cmp_to_key

...

...key=cmp_to_key(my_cmp)...