How to decide which roommate gets the bigger room

What are the ways to decide who gets the bigger room?

There are four common procedures. The first three settle who gets which room, and say nothing about the price. Only the bid method settles both.

Procedure	How it works	What it leaves out
Lottery draw	Draw numbers from a hat. Number 1 picks first, the last person takes what is left.	How much each person cares about each room
Seniority	The longest-standing roommate picks first.	Newcomers always get what is left, every time
Yearly rotation	Rooms move to the next person each lease year.	Someone leaving mid-cycle breaks the balance
Bid method	Each person privately values every room, and the best pairing wins.	It needs honest numbers and a few minutes of arithmetic

Rotation does even out the cost over time. With room prices of $900, $900 and $600, a three-year rotation averages $800 a month for each person, the same as an equal split of $2,400, but only if all three stay for all three years.

How does the bid method work?

The bid method asks each person what each room is worth to them, then finds the assignment and prices that nobody would trade. Here are the steps.

1. Fix the total. Agree the rent to be divided and that each person takes one room.
2. Write values alone. Each person writes one number per room, and the numbers add up to the rent. Nobody sees anyone else’s until all are in.
3. Try every pairing. Add up the bids for each way of handing out the rooms. With three people there are 6. The highest total wins.
4. Share the surplus. The winning total minus the rent is the surplus. Divide it equally.
5. Price each room. A room’s price is its occupant’s bid for it minus an equal share of the surplus.
6. Check for envy. Nobody should prefer another room at that room’s price.

A person’s benefit is their bid for their room minus its price. The method tries to make the lowest benefit anyone gets as high as possible.

What does it look like with three people and $2,400?

Say Ines, Owen and Kai share a three-bedroom apartment with a rent of $2,400. Each writes a value for the Corner room, the Middle room and the Back room.

Person	Corner	Middle	Back
Ines	$1,000	$800	$600
Owen	$900	$800	$700
Kai	$800	$1,000	$600

Each row adds up to $2,400. The six ways to hand out the rooms, with each pairing’s bids added up, are:

Corner	Middle	Back	Total of bids
Ines	Kai	Owen	$2,700
Owen	Kai	Ines	$2,500
Ines	Owen	Kai	$2,400
Owen	Ines	Kai	$2,300
Kai	Ines	Owen	$2,300
Kai	Owen	Ines	$2,200

The top row wins at $2,700. The surplus is $2,700 minus $2,400, which is $300, or $100 each. Each room’s price is its occupant’s bid minus $100.

Person	Room	Bid	Price	Benefit
Ines	Corner	$1,000	$900	$100
Kai	Middle	$1,000	$900	$100
Owen	Back	$700	$600	$100

The prices add up to $2,400. The envy check passes, because every other room at its price is worse than what each person already has.

• Ines: the Middle room is worth $800 to her at a $900 price, a $100 loss. The Back is worth $600 at a $600 price, a benefit of $0. Her own room gives $100.
• Owen: the Corner is worth $900 at a $900 price, a benefit of $0. The Middle is worth $800 at $900, a $100 loss. His own room gives $100.
• Kai: the Corner is worth $800 at $900, a $100 loss. The Back is worth $600 at $600, a benefit of $0. His own room gives $100.

Nobody would swap. Splitting the surplus equally does not always pass the envy check. When it fails, the researchers’ method picks other prices, and a calculator is the practical way to find them.

What happens when two people want the same room?

The pairing with the highest total decides it. In a fight over one room, that favors whoever loses more by moving. Ines and Owen both rank the Corner first, with bids of $1,000 and $900. Moving to the Back room costs Ines $400 of value (from $1,000 to $600) and Owen $200 (from $900 to $700). The pairing that gives Ines the Corner keeps the larger total, which is why it won.

Now say Owen had written the same bids as Ines, $1,000, $800 and $600, and Kai wrote $700, $1,100 and $600. Two pairings tie at $2,700, one with Ines in the Corner and one with Owen in the Corner. The prices come out at $900, $1,000 and $500 either way. Whoever has the Corner pays $900 for a $1,000 room. Whoever has the Back pays $500 for a $600 room. Kai pays $1,000 for a $1,100 room. All three are $100 ahead.

A tie costs nobody anything, because the prices come out the same. When two people want the same room, use this order:

1. Compare what each person loses by moving to the same other room. The larger loss keeps the room.
2. If that is level too, draw lots in front of everyone.
3. If you like, give the person who lost the draw first pick when the lease renews.

Is the bid method fair?

The method comes from published research. Gal, Mash, Procaccia and Zick study how to assign rooms and divide rent, and they define a solution as envy free when each person is at least as well off in their own room at its price as in any other room at that room’s price. They note that an envy-free solution always exists.

Among the many envy-free outcomes, they pick the one that maximizes the lowest benefit anyone gets. They report that Spliddit, a not-for-profit fair division website, put that version of its rent tool into use in April 2015. In a study of Spliddit users about their own real rent divisions, people rated these prices as significantly fairer than arbitrary envy-free ones.

The limits are real. The paper assumes one person per room, and its authors note that no envy-free method can also promise that exaggerating never helps. They believe it rarely matters in practice, in part because on Spliddit each person enters values separately and does not see anyone else’s.

How do you set the result up in EvenOut?

Create a Household group (“Rent and bills”), add the three of you and enter the rent as one expense with “Exact amounts”, typing $900, $900 and $600. Under “Photo, repeat, pending or note”, set “Repeat” to “Monthly”, and EvenOut adds each later month as a normal expense. Settle with “Settle up” and “Record payment”. EvenOut records who paid and who owes, and it does not move money.

What should you do next?

Pick a procedure before anyone looks at the rooms, and write the choice down. If you already have room prices from a feature score, how much more the master bedroom should pay covers that, and the room choice then comes down to a draw or seniority. What to include in a roommate agreement has a line for it, and how to split rent by room size is the simpler alternative when sizes decide the price.