2011/02/19

Rent splitting mechanism

I just came across this blog post on "How to split the rent?". Most people split the rent equally between apartment mates. The problem is that not all rooms are equal. How do you value their differences in size, light, accessibility. How do you value the shared areas? Further, different people have different preferences. So it's an interesting problem... so how do you find a fair price and allocation of rooms?

It reminded me of a solution my roommates and I came up with many years ago. It's basically an auction. Say there are 4 apartment mates, 4 bedrooms, and the total rent is $1000. Each roommate writes a bid with prices for each room, with the condition that the total has to be $1000. So the bids might look like
- person 1: ($200, $250, $250, $300)
- person 2: ($100, $250, $300, $350)
- person 3: ($250, $250, $250, $250)
- person 4: ($150, $200, $250, $400)

Then you gather all the bids and you assign each room to the person who has the highest value for it and they pay the average price of that room in all bids. You start with the highest priced room and go down (so that if a person wins two rooms you give them the one with the higher price). If you have a tie for first place on two different rooms with the same two people, you flip a coin. In the above case, no coin flip needed, the solution is:
- room 1 goes to person 3, for a rent of (200+100+250+150)/4 = $175
- room 2 goes to person 1 for $237.50
- room 3 goes to person 2 for a price of $262.50
- room 4 goes to person 4 for a price of $325

The beauty is that the solution guarantees that each room goes to the person who values it the most, and the room prices add up to the correct total rent.

We did it for one year with a 4 bedroom apartment with 4 co-tenants. The biggest room went for about 31% of the total rent, and two rooms of smaller size but with the most light went for 25%, 24% and the dining room converted into a bedroom went for 20%. The second year we were down to three tenants and for a variety of reasons, we did a direct adjustment rather than rerun the auction...

But the moral of the story is that mechanism design works in every day life! Surprisingly not many people do this.

2 comments:

  1. I was thinking what if I was bidder Z and I wagered (1,333,333,333) would this game the system? Then, I figured out (via some fancy maths) that it was a fair system quickly. Agree, most people don't live like this, at least some do.
    /j u kno who

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  2. It's cool that the sum of the averages adds up to the total rent. A bit of quick algebra shows why that is, but it surprised me at first.

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