score:27
The painting shows Robert Walpole in his full regalia as First Earl of Orford. The "crown" is not, in fact technically a crown, but rather a coronet, which forms part of that regalia.
The Wikipedia article includes a series of images depicting the coronets for various British coronet rankings. I have reproduced the image of an Earl's coronet below:
The portraits of King George I and King George II that you have added for comparison also show them with their royal regalia, including their crowns, orb, and sceptre.