I was speaking with a friend yesterday about relationships. The conversation we were having was about the fact that just because your last relationship was bad and ended bitterly, how does that influence how you think about future relationships? Not all relationships end in misery, right? ("Just mine" you might be thinking...)
I suspect that the solution to this problem can be found,as always, in an unexpected place: probability theory. There is an appropriately-named statistical problem discussed by the French mathematician Pierre Simon LaPlace (1749-1827) called the “First Night in
It is the night after Adam and Eve’s first day in paradise. Together, they watch the sun rise and illuminate the marvelous trees, flowers, and birds. At some point, the air gets cooler, and the sun sank below the horizon. Will it stay dark forever? Adam and Eve wonder, What is the probability that the sun would rise again tomorrow?
Whether Adam and Eve were truly discussing this statistical conundrum, as opposed to addressing less cerebral concerns of a non-probabilistic nature, is besides the point. What is the probability that the sun will rise again?
The classic answer is that if Adam and Eve had never seen the sun rising, they would assign equal probabilities to both outcomes. Gigerenzer, in his book Calculated Risks, likens it to placing a white marble (the sun will rise again) and a black marble (the sun will not) into a bag, and picking one randomly. However, they did witness the sun rise once that morning when they woke up, so they place another white marble in the bag, which makes the probability of the sun rising the next day .66.
(Interestingly, as an aside, one might ask the question, "What was Adam's subjective assessment of the probability that Eve would still be there the next morning?" After all, she did simply just appear there, and who knows? God might just be teasing him and yank her out of the garden.)
As we, know, Adam and Eve woke from that first night in paradise to another sunny day in paradise. But what is the probability now, given two sunrises, that the sun would rise once again the next day? The answer is simple. They add another white marble to the bag, making the probability go up to .75. And the sun rises again and another marble goes in the bag, and so on. This is known as the rule of succession. Introduced by
(n+1)/(n+2)
If you are like me, and are thirty odd years old, the subjective probability that I assign to the sun rising tomorrow is quite high. Specifically it is
(365*30 + 1) / (365*30 + 2) = 10951 / 10952 = .99990869247626004. Pretty good odds. I am, in fact, relatively convinced that the sun also rises tomorrow.
But what about relationships? Does the law of succession apply here? What is the probability, given a certain number of previous relationships, that you believe that your next one is headed to splitsville? It is just like adding white balls representing sucess and black balls representing failure to a jar and selecting one.
I asked ten friends and colleagues today how many serious relationships they had been in over the course of their lives. The median value of that number was 7 – your typical friend of mine has been in 7 serious relationships (which I defined as lasting over 6 months).
What is the average person’s subjective estimate of the probability of the next relationship ending given the rule of succession? Quite simple: (7 + 1) / (7 + 2) = 8 / 9 = .888.
So is it the case that with a greater number of failed relationships, does one use the law of succession to determine whether one’s next relationship is going to fail? Maybe. This would be an interesting study to conduct – the correlation between the number of failed relationships one has had with one’s pessimism about the probability that one’s next relationship is also going to fail. Of course there are confounds up the wazoo, but it would be a fun and simple study to do on a larger scale than my ten friends.
But there is hope here. While you might suspect that your next relationship will fail with a probability of .88, that means that you also have a probability of .12 that the next one will work out. And I like that 12 percent – I might like to call it a “Hope Factor.” Sure, the hope factor diminishes after every successive failure, but by definition, this means that one can never lose hope entirely – the law of succession may asymptote very near zero, but it never quite reaches it, due to the fact that the denominator is always one greater than the numerator. Below is a figure of the relationship between the hope and despair factors by the number of failed relationships. You can see how the region of despair increases with every sucessive failed relationship, but that region of hope never quite goes away.
As they say: Hope springs eternal! And perhaps this is why it was the last evil remaining in Pandora's Box.
