Can You Use Game Theory to Pick Your Partner? More Important: SHOULD You?

The Washington Post ran an interesting article recently applying a classic game-theory problem to relationships. Ana Swanson’s article from the Wonkblog does a great job relating game theory to a large audience. But it also shows how we need to be careful in its application. An elegant solution to a random-number problem can be a mess if you apply it to the difficult (but not random) problem of picking the best partner.

The article asks, when is it time to stop dating and commit to a life partner? There is a famous problem that sounds related to this question. (It also has several catchy names and resembles the plot of many Drew Barrymore movies.) It is known as the Sultan’s Dowry (a/k/a Secretary Problem, Fussy Suitor, Googol Game). In the Sultan’s Dowry version, a commoner gets a chance to marry one of the Sultan’s 100 daughters. He never gets to meet the daughters, has to decide immediately and irrevocably for each daughter, and is told only the daughter’s number (1, 2, 3 … 100) and the size of that daughter’s dowry. He hears the size of Daughter 1’s dowry and has to immediately decide yes or no. If he says yes, the selection process is over. If he says no, he gets to hear the size of Daughter 2’s dowry. How does he maximize his chances of getting the daughter with the biggest dowry?

The Sultan’s Dowry has an irresistibly elegant solution: Decline the first 37 daughters, and marry the next proffered daughter with a dowry greater than the largest of the first 37. Then the chance that the commoner will get the largest dowry is 37%. Deciding randomly gives you just a 1% chance. Beyond 37 daughters you diminish the chance that you get the biggest dowry as every additional piece of data increases the chance you’ve already turned down the biggest dowry plus reduces your remaining choices.

The article suggests this could be applied to relationships: figure out the number of serious relationships you will have in a lifetime (the article’s example is eleven potential mates), turn down the first 37% (four) and choose the next person who is better than the best of the first 37%.

Applying the random-number strategy of the Sultan’s Dowry to relationships is appealingly simple. Unless you are already in THE relationship of your life, finding the best partner can feel incomprehensibly frustrating and random. Now you at least have a way of navigating some of the unknowns in the mystery of relationships.

The problem, however, is that the assumptions of the Sultan’s Dowry problem don’t apply to real-life dating so the solution doesn’t work. The Sultan’s Dowry problem involves random choices, and a 37% opportunity (compared with a random opportunity of 1%) is remarkable. But our relationship choices are not random. From every relationship, we learn more about what we want and where to find it. For example, you won’t spend a relationship on a person who pushed their mother down a flight of steps, but the commoner may have to decline a potential wife because the dowry is two raisins. And if he declines that bride, the next one could have a dowry of one raisin.

I don’t object to the idea of “pricing” happiness the way the commoner prices the dowries. You can and should price elements of your happiness, but they don’t randomly enter and exit your life. Use the lessons of your earliest choices to influences the later candidates in a non-random and positive direction.

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