How Cake and Game Theory can Help you Make Fairer Decisions in Life

Picture the scene — You and your friend have decided to share a cake. They grab the knife, cut it into two pieces, and then proceed to give you the smaller piece.

After recovering from the sheer betrayal of it all, you might begin to wonder…how could we have done this in a fairer way.

The fair distribution of resources is an important aspect in many areas of our lives — we must navigate it in our friendships, romantic relationships, the workplace, and society at large.

However, when it comes to sharing limited resources humans can quickly descend into every person for themselves. So how can we set the system up to motivate people to make fairer decisions?

The ‘I cut, you choose’ Principle

One way in which can motivate people to make fairer decisions is by using the ‘I cut, you choose’ principle. The ‘I cut, you choose’ principle is well-known within the field of mathematics and game theory. It is a simple and effective way of helping two parties distribute resources fairly whilst also reducing the potential for envy at the outcome. The process is simple:

• One person divides the resources into two parts
• The other person then chooses which of the two parts they would like for themselves

By giving ‘first dibs’ to the other party, the person who is dividing the resources is inherently motivated to distribute them in a fair manner, otherwise, they’ll leave themselves vulnerable to getting the worst outcome. Let’s see why this works by re-visiting our cake example:

Scenario 1: Splitting the Cake Unevenly

Adam tries to sneakily maximise the amount of cake that he can get and cuts the cake like this:

Sharon immediately spots that Adam is being unfair and chooses to take the bigger piece, slice 1. Adam is left with the smaller slice and the existential regret of trying to cheat Sharon out of cake.

Scenario 2: Splitting the Cake Evenly

Adam recognises that if he cuts the cake unevenly then Sharon will simply choose the larger piece and he will be left with the smaller piece. To avoid losing out on the cake Adam realises that he needs to cut it in a way where there are no smaller slices for him to be left with, so he does this:

Now, it doesn’t matter which slice Sharon chooses as they are both the same. The amount of cake that both Adam and Sharon can have at the same time has been maximised and it’s a much fairer distribution of the cake overall. The ‘I cut, you choose’ approach encourages the person allocating the resources to do so fairly otherwise they will be putting themselves at a disadvantage later on.

Splitting Chores Fairly — The Two List Approach

Ok, so dividing cake fairly is a pretty niche application but the same principle can be applied to a wide range of activities. For example, a common source of friction in relationships can be the division of chores.

One person may feel that they do more than their fair share or that the other person shirks the more difficult or unpleasant tasks. We can apply the ‘I cut, you choose’ principle to split chores out more fairly between partners. Let’s see how:

1 — Both partners identify all of the chores that need to be completed on a regular basis.

2 — Partner A splits the chores evenly across two lists

3 — Partner B chooses which list they would like to take responsibility for

If partner A tries to game the system by putting all of the easy chores on one list and all of the unpleasant chores on the other then partner B will simply choose the easy list. As a result, partner A would be stuck with all of the unpleasant tasks. To avoid this, partner A will be motivated to distribute both pleasant and unpleasant tasks evenly across both lists. That way, it doesn’t matter which list they get, they’ll have just as many pleasant and unpleasant tasks as their partner. As an added benefit, both partners were actively involved in the decision-making process and so it also makes it harder to say that the distribution of chores was unfair.

Not all things are desired equally: Where the ‘I cut, you choose’ principle struggles

As with all techniques, there are both strengths and limitations. Whilst the ‘I cut, you choose’ principle can be a simple way of splitting resources fairly between two parties there are instances where it doesn’t work as well.

Here are a couple of scenarios where the approach may be limited

Social pressure — think back to the opening cake example. In the real world, it would be unlikely that your friend would give you the smaller piece of cake. Why is this? Well, your friend is likely a nice person (after all, they’re your friend) but they may also be trying to avoid negative social stereotypes attached to behaviour that is perceived as being greedy. No one wants to be known as a mean or ungenerous friend. So if the ‘I cut, you choose’ division is being made in a situation where there is social judgment involved, a person may choose the worse option out of fear of being perceived negatively for choosing the better option.

Value is subjective — the principle works best in situations where both parties value the resources relatively equally. However, in the real world that isn’t always the case. For example, in a divorce settlement, one partner might not care about the value of a watch and would simply choose to sell it. However, the watch may have a high level of sentimental value to the other partner and be amongst their most prized possessions. Knowing this, the first could manipulate how the asset list is divided to secure a better outcome for themselves. This makes the ‘I cut, you choose’ principle vulnerable to exploitation when there are significant differences in the values attached to the same resources between two parties.

The ‘I cut, you choose’ principle can be a quick and easy way of sharing resources fairly between two parties. It can also help to reduce feelings of dissatisfaction with the outcome, as both parties were actively involved in the decision-making process. Whilst it has its limitations, it can be a valuable tool in your decision-making toolkit. So next time you have to divide up some resources — think cake.

If you would like to find out more about the application of game theory to everyday life then you may find the following book interesting:

(This article is not sponsored. However, the above is an affiliate link, which means that if you make a purchase through it, I may earn a small commission at no extra cost to you.)

Dr. Anthony Thompson

References

1- Brams, S. J., & Taylor, A. D. (1996). Fair Division: From cake-cutting to dispute resolution. Cambridge University Press.

2- Makowski, M., & Piotrowski, E. W. (2014). When I cut, you choose method implies intransitivity. Physica A: Statistical Mechanics and its Applications, 415, 189–193.

3- Fisher, L. (2008). Rock, paper, scissors: game theory in everyday life. Basic Books.