Well, looks like all is right except for the $675. That is not right.

Reason:
***Split three ways equally, rent would *normally* be $525 each/month. Roommate #1 and Roommate #2 each have their own room and I live in the living room. Because of this arrangement, both Roommate #1 and #2 pay $50 more a month, their rent is $575. I have a reduced rent of $100 and pay $425. These numbers, $575+$575+$425= $1575. ***

Rent is $1575 split between y'all. And you guys played with $100. So you, John, pay $525 - $100, the other two pay $525+$50 each. So you John indeed pay $150 less than any one of the other roomates, because $100 (your discount) + $50 (one roomates' extra payment) = $150.

If you want to make it where you pay $100 less than the any one of the roomates, then you have to adjust the $100 y'all are playing with.

John's discount - J
Roomate1extra payment- A
Roomate2 extra payment- B

J = A + B
where A=B
so J = A * 2
or J/2 = A
and you want J + A = 100

J = 100 - A
J = 100 - J/2
J = 200/2 - J/2
J = (200 - J)/2
2J = 200 - J
2J + J = 200
3J = 200
J = 200/3
J = 66.67

so A = B = 33.33

So your discount should be about $66.67 and each of their extra payment should be about $33.33 give or take a penny.

So your rent should be $525 - $66.67 = $458.33
And each of the other roomates rent should be $525 + $33.33 = $558.33

Check
$458.33 + $558.33 + $558.33 = $1574.99

Now all you have to do is fight over the last penny. LOL!

The problem is in the question. In it you define that roommate 1 and 2 pay 50 dollars more a month. Then you "choose" this 525 which has relevance to something, but not your definition that they pay 50 dollars more a month. Thus, you end up with a contradiction. They are on the right side.

Roommate#2 is right, she pays $150 (=$575 - $425) more then you do. But that is not her real issue, what she is really complaining about is that is that she doesn't feel that what she is paying is FAIR. Fair is what the three of you negotiated when you moved in. If she doesn't like that, I think what you've described is fair and reasonable, she can move out.

To be fair, one must do what you've done:

RM#1 = $(x + (total rent/3))
RM#2 = $(y + (total rent/3))
RM#3 = $( (total rent/3) - x -y)

RM#1 + RM#2 + RM#3 = total rent

Where x and y represent the "value" of the space that RM#3 doesn't get by living in the living room. X and y don't have to be the same because the value of the space that RM#1 and RM#2 don't have to be the same, say RM#1 had a master bedroom but RM#2 only had a bedroom.

Eric's logic only holds only if the value of having a bedroom is twice that of not having one. What your roommates agreed upon is that the value of not having a bedroom is trice (3 times) that of having one.