I have a math question concerning a bill.?

The two who under paid are due nothing, and in fact still owe the amounts they under paid. The person who over paid covered what the other two should have paid and that room mate is owed $22 from one and $72 from the other. What makes you think that if you didn't pay your bull in full that you should be due some sort of a refund for money you did not contribute. And how is it that 3 people split a bill 4 ways, is there an invisible person who pays 1/4.