# Probability of finding true love

The concept of true love has been invented by poets and other exaggerators. Evolutionarily, the optimal strategy is to settle with a good enough partner, not to seek the best in the world. But suppose for the sake of argument that a person A’s true love is another person B who exists somewhere in the world. What is the probability that A meets B?

There is no a priori reason why A and B have to be from the same country, have similar wealth or political views. Isn’t that what poets would have us believe – that love knows no boundaries, blossoms in unlikely places, etc?

Given the 7 billion people in the world, what fraction of them does a given person meet per lifetime? Depends on what is meant by “meets” – seeing each other from a distance, walking past each other on the street, looking at each other, talking casually. Let’s take literally the cliché “love at first sight” and assume that meeting means looking at each other. A person looks at a different number of people per day depending on whether they live in a city or in the countryside. There is also repetition, i.e. seeing the same person multiple times. A guess at an average number of new people a person looks at per day is 100. This times 365 times a 70-year lifespan is 2555000. Divide 7 billion by this and the odds of meeting one’s true love are thus about one in three thousand per lifetime.

Some questionable assumptions went into this conclusion, for example that the true love could be of any gender or age and that the meeting rate is 100 per day. Restricting the set candidates to a particular gender and age group proportionately lowers the number of candidates met and the total number of candidates, so leaves the conclusion unchanged.

Someone on the hunt for a partner may move to a big city, sign up for dating websites and thereby raise the meeting rate (raise number met while keeping total number constant), which would improve the odds. On the other hand, if recognizing one’s true love takes more than looking at them, e.g. a conversation, then the meeting rate could fall to less than one – how many new people per day do you have a conversation with?

Some people claim to have met their true love, at least in the hearing of their current partner. The fraction claiming this is larger than would be expected based on the calculations above. There may be cognitive dissonance at work (reinterpreting the facts so that one’s past decision looks correct). Or perhaps the perfect partner is with high probability from the same ethnic and socioeconomic background and the same high school class (this is called homophily in sociology). Then love blossoms in the most likely places.