In “The Calculus of Happiness,” math professor Oscar E. Fernandez presents a simple formula for splitting a sum fairly with someone else.
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Imagine: You and your partner have the same five days off from work.
Each of you wants to spend the whole five days alone, apart from the kids. But you can’t very well leave the little rascals parentless. How should you split up the five days fairly?
This might sound like an issue for a couples therapist. In fact it’s a problem that can be solved pretty quickly using math.
That’s according to “The Calculus of Happiness,” a new book by Wellesley professor Oscar E. Fernandez. In the book, Fernandez presents mathematical equations that can help you figure out how many calories to consume, when you’ll hit financial independence, and how to resolve the most common relationship dilemmas.
The formula for making optimal joint decisions is based on a 1950 paper titled “The Bargaining Problem” by John Nash (the protagonist in “A Beautiful Mind”).
Fernandez adapted the equation from Nash’s paper and came up with a neat formula. Before I share it, let me say that there’s a handy online calculator that can do the math for you. Now here’s the formula:
Your share of the vacation days = T/2 (1 +Yd/M – Pd/N)
Your partner’s share of the vacation days = T/2 (1 +Pd/N – Yd/M)
If you’re not a numbers person, don’t freak out. Once we break down what each of these letters means, it’ll seem a lot simpler. So here goes:
T is the total sum. In this case, that’s five days.
M is your happiness level if you were to get all five days to yourself (on a scale of 1-10).
N is your partner’s happiness level if they got all five days to themselves.
Yd is your happiness level if you two weren’t able to reach any agreement on how to split the five days.
Pd is your partner’s happiness level if you two weren’t able to reach any agreement on how to split the five days.
Let’s say your happiness level if you were to get all five days off is eight and your partner’s is 10. And let’s say your happiness level if you two weren’t able to reach any agreement is four and your partner’s is three.
Plug those numbers into the formula and you see that you should get three days off and your partner should get two.
Fernandez highlights a cool implication of this formula: A simple way to get a bigger piece of the pie is to start feeling happier about the possibility that you two won’t reach any agreement. In other words:
The more willing you are to walk away, the more negotiating power you have.
As Fernandez points out in other parts of the book, this formula assumes that you’re able to quantify your feelings — and that your feelings won’t change over the course of the negotiation. So it won’t work perfectly every time.
Still, it’s one example of how you can outsource a messy life task to a calculator (or a pen and paper, if you’re so inclined). Another example is an algorithm that can help you find your soul mate — an idea that people are notoriously resistant to.
If nothing else, these formulas are a nice reminder that our interpersonal issues probably aren’t unique. Other people have not only encountered these problems, but they’ve also come up with ingenious ways to solve them — at least temporarily.