How to split rent between roommates

I noticed recently that the bill tracking tool SplitWise has a rent splitting calculator.  In a blog post explaining how it works, they talk about the various ways people use to split their rent.

Rentsplit

A Google search on how to split rent yields rather some bland suggestions like paying based on square footage.  I also know pairs of roommates, who decided they would just pay equal rent but switch rooms halfway through the lease term.

All these ways suck.  There is an extremely fair way to split rent and it’s to split based on the value of each room for each person.  And this method guarantees that each person will get a room for less than what they’d be willing to pay for it.

The Process

  1. Each person writes down what they think the value of each room is. Or to put it another way, each person writes down a proposed split at which they’d be okay getting any room.
  2. The proposed splits are averaged to calculate the value of each room.
  3. The rooms are assigned based on who proposed a higher value for each room.

Let’s go through an example.

Say Harry and Ron are looking to get a $1000 apartment together in the city.  Harry would be willing to pay up to $600 for the bigger room, so he’d propose a $600-$400 split.  Ron, however, really wants the big room and would be willing to pay up to $700 for it, proposing a $700-$300 split.  Putting these together, the larger room is valued at $650 and the smaller room at $350.  Since Harry wouldn’t want to pay $650 for rent, the former would go to Ron and the latter would go to Harry.

Notice how both get a better deal than they would have settled for.  Ron would have paid up to $700 for the larger room but now gets it for $650.  Harry would have let Ron have that room for just $600, and paid $400 for the room he now gets at $350.

You can’t cheat the system

Can either party try and make a proposal to cheat the system?  The answer is only if they know what the other party was going to propose, and even then, not by much.  For instance, if Harry knows that Ron would propose a $700-$300 split, he might propose a $690-$310 split so that he ends up getting his smaller room for just $305.  But even then, Ron still gets his master bedroom for a lower price than he was willing to pay for it.

More than 2 parties

What if there are more than 2 parties?  Same thing.  Suppose Hermione also wants to live with her besties, and they find a slightly larger apartment that’s advertised to be 3 bedrooms (but the third room is actually a cupboard under the stairs).

Now, each person might offer up a split like this.  Each person proposes a split and averaging all three gives each room its established value.  (Harry really doesn’t want to relive his childhood and refuses to live under the cupboard unless he gets it for free.)

Master bedroom Smaller bedroom Cupboard under the stairs
Harry $774 $726 $0
Ron $750 $550 $200
Hermione $600 $500 $400
Established Value $708 $592 $200

In this case, both Harry and Ron have proposed getting the master bedroom for more than its value.  But only Harry proposed paying more than $592 for the smaller bedroom, so he gets it for that much.  This means Ron gets the master bedroom for $708, and Hermione gets the cupboard for $200.  Once again, everyone gets a room for less than they’d have been willing to pay.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s