# A New Formula for the Rent-Splitting Problem

We’ve addressed the rent-splitting problem before. Now, Harvard astrophysics grad student Jonathan Bittner is seeking to solve the problem with a rent calculator to help roommates approximate fair prices in this “market.” The web tool uses a formula designed by Bittner (informed by a survey of his friends) to calculate how much each renter should pay based on room size, windows, closets, but also more detailed elements such as noise from street and whether the room has an awkward layout. Bittner writes on his site: “The idea is that you should pay the ‘market’ rate for these amenities (or get a market discount for annoying things) without having to think too hard…I like formulas, I like surveys, I like fairness, and I wanted to make something on the web. There’s something both fun and funny about using a mathematical way to decide what is fair.”

#### Sam

Very interesting factors, but has anyone considered other factors that aren't related to the space, but the contributions of the roommates to the apartment? For example, what if one roommate finds an apartment, negotiates and significantly lowers the price of apartment and then finds another roommate to cohabit the apartment with him? Should he share the savings he negotiated with incoming roommate? What if a roommate does all the billing, pays the bills upfront and manages all the dealings with the apartment? What if a roommate's furniture contributions to the apartment are a lot higher in value than those of the other one? I think these should all be taken into account when writing any formula about calculating fair prices.

#### ryan

how is it that, in neither this post, nor the prior linked post, any of you freakonomists brought up the simplest and fairest way to split rent - an auction? starting with the 'best' room, everybody bids until the highest WTP renter gets it. then, subtract that rent from the total, and start the bidding for the next room at the average remaining price. no one can complain, because everyone ultimately chose their rent (with the constraint that the total rent actually needs to be paid).

we did this in college, and not only was it a fun way to spend a few hours, i also ended up with the smallest room (which was basically a closet) at an incredible markdown, which would have been considered totally un'fair' if we were drawing up rent prices beforehand and divvying up.

#### Jkim

The best solution is for people to bid for the most coveted room in an auction system.

A formula ignores individual preferences.

#### Emily

Sam, I've got to disagree with you, especially when it comes to furniture contributions. Unless roommates are doing damage to the furniture (in which case you've got a separate issue), it shouldn't be factored into the rent. Capital purchases should either remain the property of the person contributing them, or other roommates should pay a cost up-front to share ownership (if, for example, they plan to sell the furniture and split the proceeds when they all move out).

I also think that something like negotiating a rate up front is a sunk cost to the person who negotiated.

Finally, when it comes to managing the dealings with the apartment, that's an arrangement that should be made outside of a calculator for per-room rates. If a person lives with 4 other people, and thinks he spends about \$20 worth of his time dealing with apartment stuff per month, he should simply request that he pay \$20 less and everyone else pay \$5 more.

#### steve

I have done the same for my house based on floor area of the house, split according to how it is shared, i.e. 4 share the living areas, 2 share 1 bathroom while the other 2 have their own bathrooms. I came up with it because someone's partner moved in to their room so had to work out their share of the whole place. actually worked pretty well for our existing rents too.

#### Ulysses

How about just not being such a penny-counting cheapskate?

#### Steven

The calculator works great for me. I live with two other guys, and our rooms are all of different sizes. The calculator gave us results to within 3% of how we actually decided to split the rent at the beginning of the year.

#### Larry Waybright

Weighted averages based on real contributions does sound reasonable to me.
I would not find it reasonable for one room mate to pay all the monthly costs until the other(s) have already paid the one who writes the checks their share. There are inexpensive power consumption devices that can determine how much of the power bill should be adjusted based on how much an unusually power grabbing hobby adds to the basic electrical and other metered services amounts to a fair share, too. These calculations must be adjusted as data is collated over time.

The "finders fee", for lack of a better phrase can be a one time cost adjustment but must be paid upfront because a room mate may move out before enough time has passed to amortize those costs.
The program's formulas can be made to reflect these factors in the pre-agreed parameters.
It is unfair for the person who brings the most assets which everyone uses equally, to absorb all the depreciation. That should be factored in.
Anyone who participates in sharing the same space must agree what the formula is first. Simply dividing the bills equally but not having to pay anything for the valuable assets and wear and tear on the property should be prorated by what each brings to the common areas of the house hold.
It still would be cheaper than bearing the entire costs of an abode alone.

#### Matt

I would have thought an auction set up would work just as well. Let the roommates bid on the rooms and it avoids the need for a formula altogether.

#### Ian Kemmish

"Fair" is one of those words which has six milliard different meanings, isn't it? There's no way a randomly selected group of youngsters are going to agree on the value of an extra square foot of floor space compared to a west-facing window.

The value of this system, if it has any, is not that it's fair, but that it's a set of rules proposed by someone - anyone - who isn't actually living in that house. Having the landlord come in and tell everyone what they're going to pay would probably work just as well. Probably better, as those dissatisfied with their lot wouldn't then waste time inventing a "better" calculator....

#### Ross Parker

As mentioned by a previous commentator, an auction is an efficient mechanism.

However, I would not auction rooms, but the ranking of picking rooms. I.e. You bid for the right to pick a room first, second, third (to n-1 where n is the number of rooms, as the right to pick the last available room has zero value).

If you wanted to get fancy, you could auction rights on a second-price basis to avoid the winners' curse.

If you wanted to get fancier still, you'd run this auction every month - preferences may adjust with improved information about what it's like to actually live in a room.

#### Jeff D

Bittner points out at his website that an auction is a great way to split the rent, but notes there are reasons/situations where people would prefer not to do it this way. Also, while auctions are generally fair, they do give an advantage to those with better gaming skills (if you don't believe that then invite a novice to your fantasy baseball draft). In many aspects of life it is okay to "beat" others because of better gaming skills, but for many (including frequently the "winner") this would not work well in a shared living arrangement. I think it is a brilliant idea that at least gives roommates an equitable option for rent allocation.

#### ryan

@Ross Parker - can you explain when your system would result in a better outcome than simply auctioning off rooms? if i have idiosyncratic preferences (say, i really want the room with no windows), i probably know that, so i'd rather wait and get the room for cheaper than bid high to ensure i had the chance to pick the room. the resulting prices, if different at all, would reflect the participants risk aversion more than the relative quality of the rooms.

also, a second-price auction (which, when talking about economically efficient auctions) usually means seled bids. Since there is a total rent number you need the bids sum to, i don't think it would make sense here.

#### Ross Parker

@Ryan - You'd auction choice positions rather than places because in a situation with three rooms and three flatmates, you have two choices for auctioning:

1. Simultaneous room auctions
2. Auctioning the rooms in turn

Simultaneous room auctions are problematic. Say I want room A or B, and I really don't like C. Do I bid hard for A and B at the same time? What if I win both? Do I pick? Re-auction the least favourable (to me)?

Auctioning rooms in turn gives me another problem. What if I exit bidding on room A, thinking I will have a better chance at Room B, but miscalculate other's preferences?

Auctioning room choice rankings avoids these dilemmas. If I want room A or B, I know I have to bid for at least the right to pick second. If I want just room A, I know I need to bid for the right to pick first.

#### Ross Parker

Also, I don't think there ought to be "a total rent number you need the bids to sum to".

You agree on 1/3 rent each at the outset. The room auctions are a secondary round of redistribution.

You can't confuse the overall rent level negotiation between the collective and the landlord with the distribution of resources within the collective.