This post is based on the following email I got from Cheryl:

Hi Presh~ Could you write a blog post on game theory tips for fairly dividing household chores/tasks (for roommates, partners, and perhaps coworkers)? Bonus points for providing easy division methods that people will actually use. In any case, keep up the good work. Thanks.

I thought this was a great question and I wanted to take stab at it. Here are a couple of ideas I came across the following two ideas.

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"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

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Method 1: “I cut, you choose”

This is one of the most famous examples from fair division. Let’s imagine that two people are trying to split up a triangular slice of cake, but they might have different preferences for the filling or whipped creme topping. What’s the fair way to divide the cake?

The answer is astonishingly simple: one person gets to cut the cake, but the other person gets to choose his piece first. The idea here is that the person cutting will be encouraged to make the pieces as equal as possible so that he ends up with a good piece. If he makes one piece too large, then the other person will just take it, leaving him with a small piece.

This cake-cutting problem is generalizable to all sorts of areas, as I have written about before in a peanut butter commercial and in terms of splitting a can of Coca Cola.

In cake-cutting, the goal is to get as large a piece as possible. For chores, the problem is exactly the opposite: you want to pick the smallest “piece” that corresponds to the least amount of effort.

The problems are analogous, and the “I cut, you choose” method works very well here. Here is how you can divide up chores between 2 people:

Let one person divide the chorses into two separate lists. Let the other person choose the which list to do.

The idea will work out in a very similar way. The person who makes the list of chores has to make the two lists as equal as possible. If not, the other person will choose the easier set of chores.

The “I cut, you choose” method is great for 2 people. It can be extended to 3 and 4 people, but those scenarios can prove to be a lot harder. For details, see this paper about fairly dividing up chores for 4 people.

Method 2: Tug-of-war method

The “I cut, you choose” method is great for infrequent chores like taking out the trash or cleaning the gutters. But it is not so good about dividing up daily chores like cooking.

If you’re in a house where you wish to split the job of cooking, what is the best way to do that?

The idea is you want to split up the amount of work and have some way that both people can agree to the commitment.

I came across a very interesting idea from a webpage posted in 1993. The author turned out to be the economist Robin Hanson who writes the interesting blog Overcoming Bias.

Here is Hanson’s advice found on this page:

When both my wife and I were employed, we split the task of cooking (or picking up) the evening meal with a “Tug-O-War” board, like: --------------------------------------- |h /#\ | h| |i 0 0 ### 0 0 0 0 e| |m \#/ | r| --------------------------------------- This has a row of seven holes, with a peg sitting in one of them. The rule is that when you cook, you get to move the peg one step in your direction. If the peg gets all the way to your end, the other person *has* to cook. Now you can cook a few nights in a row if you feel energetic, or wait a few nights if you’re sick. If neither of you wants to cook, the person farther down is expected to cook.

The tug-of-war method is interesting to me for a couple of reasons.

First, with a daily chore it is very hard to remember who has done the work. Each person has a bias towards thinking they have done more of the cooking than they actually have. The board is an unbiased way to keep track of the work, and each person can see the results day by day.

Second, the board has a commitment rule so encourage the work split to stay near equilibrium. If one person has done too much of the work for the past few days, the other person knows it too, and will have to make up for the cooking.

The same technique can be generalized for more people. Instead of a single board, you make several columns with each person’s names. Everyone starts out in the middle, and each time you do a chore, you move your marker up and everyone else’s marker down. Anyone who is at the bottom has to do the chore, and anyone at the top does not have to.

I’m sure there are other interesting ideas for splitting up chores. How do you divide up work in your house?

Classroom discussion questions

1. Let’s say two roommates agree to a division of chores. Suppose one roommate decides to hire help rather than doing the work. The other roommate feels this is unfair because he cannot afford to hire help. Is this a valid complaint?

2. How might you penalize someone for not doing their chore?

3. One roommate feels the kitchen floor should be mopped every two weeks, while the other thinks a month is fine. What is a fair way to decide how often to mop, and who does the mopping?