The Logarithm of Love (Ice Cream Headache)


In 1960, Smokey Robinson’s mama dropped some serious truth when she insisted he better Shop Around. Given the decade, Smokey probably assumed her wisdom came from a woman’s deep understanding of bargain shopping, but I prefer to think she was simply keeping up with modern trends in mathematics.

Around that same time, numbers guys around the world were turning their attention to a decision-making dilemma they dubbed The Secretary Problem (also The Marriage Problem). Since the parameters of the problem are applicable to many real world situations, and since I choose not to indulge the sexist world of the Mad Men era, I call it the Ice Cream Headache.

Imagine yourself in an ice cream shop facing dozens of flavor options. You have to decide on just one, and ideally you want to choose the very best of all. The rules are simple: first, your choices are finite. (Even though Baskin Robbins lies and offers more than 31 flavors, they still don’t offer “infinity” flavors.) Second, you can sample flavors, but only one at a time, only once each, and you must make a decision immediately upon tasting – choose it, or pass. Finally, there are no ties. One is decidedly the best (for you).

To maximize your chances of walking away with The One, it turns out “shop around” really IS the best strategy – to a point. Mathematicians came to find that the optimal approach is to always reject the first 36.7% of flavors you try (that happens to be 1/e for all you natural logarithm fans out there), then choose the next flavor that tastes better than anything that has come before.

Say there are nine flavors total. This optimal method means we will taste the first randomly selected three and not choose them, no matter what. The odds of The One being in those first three (which means we will definitely NOT win the game) is 33%. The other 67% percent of the time, we still have a chance.

After rejecting the first three, we will choose the very first flavor that tastes better. If we happened to taste the second best flavor in the first three but not The One – the odds of which is 25% – we are guaranteed a win. Only The One will taste better, so only The One will be chosen, no matter how long it takes us to get to it. The remaining 42% of the time, victory depends on when in the subsequent tastings The One appears.

When the math is said and done, probability shows that employing this strategy to the Ice Cream Headache results in victory – choosing The One – at minimum 37% of the time, which is the best chance possible and far better than choosing at random.

Sure, in real life we are free to piss off the ice cream vendors as we test every single flavor over and over until we are either satisfied with our decision or just satisfied, but the parameters of the Ice Cream Headache are remarkably realistic when it comes to dating.

In love, we generally get one shot at evaluation – Burton and Taylor notwithstanding. Likewise, the choice is usually a now-or-never situation. (We may dream of “sampling” a person and then getting to try all the other people too before ultimately deciding, “You are the best,” but in reality that ends with a “Screw you, I’ve moved on” and a drink in the face.) Finally, even with today’s online resources, we still have a finite number of candidates.

Applying the lessons of the Ice Cream Headache to a partner search yields some interesting results.

For one, it helps redefine the idea of “success”. We usually view situations as win or lose, but mathematics has a third option: draw. Victory in the Ice Cream Headache is walking away with The One, but failure isn’t everything else; failure only happens if we walk away with a flavor that is NOT the best. Remember that 33% chance The One was in the automatically rejected first group? In that case, the player would never choose any flavor, because nothing would ever meet the requirement of outperforming everything prior. In life terms, the player stays single. I like the idea of a single life being a “draw” rather than a loss.

More significantly, the Ice Cream Headache validates the practice of living a little before settling down. The average life expectancy of an American woman is 82 years; 77 for American men. If we apply the “discard the first 36.7%” rule, no one should even consider choosing a life partner before age 30 or 28, respectively.

To apply the strategy more specifically to our dating years, let’s say no one dates seriously before 15, and we reserve the last 10 years for writing memoirs and bowling. That leaves 57 shopping years for women, and 52 for men. Again, if we automatically pass on the first 36.7% of candidates, that translates to 20 years of dating before possibly making a choice (19 for men). Starting at 15, that pushes the start of decision time to our mid-thirties.

Yes, this simplifies things with the premise that potential mates will appear at a steady rate across our dating years (now more likely with the internet), but the end result is still valid. Statistically, the optimal strategy over a lifetime for successfully ending up with your ideal flavor is to not get serious about choosing until sometime after 30. Mama was right: you better Shop Around.

Of course, this still doesn’t solve the problem of that awesome mocha chip gelato you finally go for deciding he doesn’t want you. But it helps.


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