We'll do it this way then...
If both artists in a group votes on their own pieces, it will count as a 1/2 vote. (i.e. if you vote 10 on your own piece, it will be marked as 5)
If only 1 of the 2 artists in a group votes then their vote will be removed at the end of the voting round.
And if you don't like this alternative, well you're just gonna have to suck it up, buttercup.
This seems unecessarily complex and still doesn't solve the problem at hand. Consider now that you've got 4 people - 2 people in a group A, and 2 people in group B. So, the 2 people in group A vote for everyone - lets say everyone gets a score of 20, for simplicity. Then the people in B don't vote. However, now, with this system, each artist in group A will only have a score of 10, while the people in group B who didn't vote (but had others vote for them) have a score of 20. There's a problem here.