Medic is short with judges with college degrees (10)

'college degrees' is the definition.
'doctorates' can be an answer for 'degrees' (doctorate is a kind of degree). I'm not sure about the 'college' bit.

'medic is short with judges with' is the wordplay.
'medic' becomes 'doctor' (I've seen this before).
'is short' means to remove the last letter.
'with' means one lot of letters go next to another.
'judges with' becomes 'rates' (rating is a kind of judging. I am not sure about the 'with' bit.**).
'doctor' with its last letter removed is 'docto'.
'docto'+'rates'='DOCTORATES'

Can you help me to learn more?