Flirting — An Exercise in Bayesian Statistics

The rituals of courtship are as numerous as they are odd. A fake laugh at something that wasn’t even funny. A flipping of hair. A corny pick-up line.

What does it all amount to?

The answer lies in Bayesian statistics, for flirting can be seen as nothing more than an exercise in making observations and then updating prior beliefs accordingly. Flirting is two things at its core:

1) Trying to figure out if someone likes you or not (or if they would make a good partner or not) by observing their behavior/signals when they are around you.

2) Sending signals to someone else in the hopes that they pick them up and reach the conclusion you want them to reach (that you are interested in them or that you would make a great partner).

Let’s break this down in a more formal way, with the help of Bayes’ Theorem. Here it is below:

Image result for bayes rule proportional
The foundational theorem guiding this essay

What does it mean? Let’s break it down. Let’s look at the two variables in the equation — Θ and data. We can think of Θ as an outcome. We start with P(Θ), which we call the prior, and the meaning of P(Θ) is pretty straightforward — it’s what we believe the probability is that our outcome actually happened. Here’s a real example to clarify. Let’s say that Θ is the outcome that a flip of a coin lands on heads. Let’s say our prior belief — what we start out believing before any data is observed — is 50%. This means that our prior belief is that the probability of the outcome of a coin flip being heads is equal to 50%. P(Θ) = P(Outcome of coin flip = heads) = 50%. The prior can essentially be anything — it’s whatever you start out believing. In this case, my life experience and common sense cause me to think P(Θ) = 50% is a reasonable prior, and I hope you agree.

Now that we have our initial beliefs, P(Θ), set, let’s bring in the next part of the equation, P(data|Θ). This is simply the likelihood of observing certain results/data if we take our prior distribution for θ to be true. So we have the prior P(Θ) = 50%. P(data|Θ) is saying that, given that a coin is fair (the outcome being heads is 50%), the probability of observing some data is P(data|Θ). That data is whatever we actually see — for example, if we observed 30 coin tosses and 30 came up heads, then P(data|Θ) = P(30 heads in 30 tosses|Θ = 0.5) → how likely is it that we got 30 heads in 30 tosses if the coin was indeed fair? How likely is it that the observed data arose from the prior? It should be clear that the likelihood of 30 heads in 30 tosses happening is incredibly low if the coin was indeed fair. P(data|Θ) = P(30 heads in 30 tosses|Θ = 0.5) is almost 0.

Bringing it all together, P(Θ|data) is our posterior belief after observing the evidence. It can be seen as updating our prior belief according to what we observed in the data. In the context of the example, what this means is basically that we’re updating our prior belief that the coin is fair to a new posterior belief that the coin favors heads. This is just common sense — we start out thinking the coin is fair, then we see that it comes up heads 30 times in 30 tosses, and then now we believe the coin is less fair than we initially thought and instead more biased towards heads. Clearly, from the train of logic we just followed, we see that the posterior is proportional to the prior times the likelihood of data arising from that prior. Mathematically, P(Θ|data) α P(Θ) * P(data|Θ).

Fair or not? Observe data and use Bayes’ Rule to find out

Great, now we understand Bayes’ Rule. If you think about this, we actually implement Bayes’ Rule in our thought process all the time. If we think something is true, and then we see data that affects that prior belief, we change our initial beliefs in some way. If I think Bob is a stingy person, and then I see him give money to a beggar on the street, I revise my initial belief that he is stingy to a new belief that he is not as stingy as I had once thought — because the likelihood of Bob giving money to a beggar if my prior belief that he is stingy is true is low, which makes the posterior belief tend closer to one of Bob being less stingy than before. Every time you change your mind because of new evidence, you’re using Bayes’ Rule.

So what does this have to do with flirting? You’ve probably guessed it by now. Flirting is a high-stakes, emotionally-charged manifestation of Bayes’ Rule. There are a couple of ways to think about this.

First: you want to figure out if your love interest likes you back. You start out with a relatively uninformed prior, just a random guess as to whether or not they like you. Maybe you had a bad first impression, and you set your prior at P(they like me) = 25%. That’s way to uncertain for your taste to go declaring your love. You want more information first.

So you hang out more, you go on dates, you see each other more often, and in each of those instances you’re collecting data. Maybe they hugged you tightly — the probability of that happening if there was a 25% chance they liked you is pretty low — maybe you underestimated yourself in the beginning and now you update your prior of 25% to a posterior of 27%. Maybe you touched them and they instinctively recoiled in disgust → update that prior and reduce it to maybe 5%. And on and on we go.

This guy will update his prior belief on whether the woman likes him after he sees how she reacts to this touch

You’re gathering all this data, observing their every move, and plugging them into Bayes’ Rule in the hopes that you’ll get to update your prior in an upwards direction. Maybe one day you feel like you’ve collected enough data and say that yes, the probability that they like you is actually really high — it’s time to confess your feelings! Or maybe one day you’ve come to the conclusion that the probability they like you is terribly low, and now you know you should give up and move on.

Either way, every time you date, you’re unconsciously using Bayesian inference. And so is the other person. They’re evaluating you and your behaviors in the exact same way. You want to guide them in the right direction and help them update their prior accurately — so you give a flick of your hair, touch them on their forearm, etc. Or, if you’re not interested, you give them the cold shoulder, walk out of the date, etc. Get them closer to the conclusion that you want them to get to.

Second: The same Bayesian calculation can be done for the other purpose of flirting — to evaluate the quality of a potential partner or to signal one’s own quality. When you see them tip the waiter well, you revise the prior to reflect that data — your belief updates into one that says they’re a better person than you initially thought. And the reverse holds true if your date screams at the waiter for bringing the dish out 2 minutes too late.

With this knowledge in hand, we can now see the keys to flirting. They are as follows:

1) You need to gather data. It’s the only way to be more informed. So go interact with your crush!

2) Your success is dependent on how good you are at estimating/calculating the P(data|Θ) term — you need to figure out how someone would be expected to act if they liked you and how much your observations differ from that expectation.

a. To help in this calculation, ask your friends to analyze the situation. When we ask our friends for advice, all we’re doing is refining our calculation of P(data|Θ)!

3) Update the posterior accordingly. Hopefully the data will show that they like you more than you once thought!

Hopefully this was helpful — take Bayes’ Rule with you, and best of luck with your romantic endeavors.