Call Me Maybe - An Analysis & Defence

I have spent today clearing out old files, and came across a detailed analysis I onnce wrote of the rationality of  the main character in Carly Rae Jepsen's Call Me, Maybe. Start your 2021 off right by seeing what 2012 me thought could be said in defence of the rational good standing of this pop song classic.

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Recently a friend brought my attention to the following analysis (see this as well) of the hit song Call Me Maybe by Carly Rae Jepsen. I think both analyses quite fundamentally mistaken, and since I am a fan of the song I think it deserves better. So here’s my own crack at the whip. Note that I will follow the blog post in taking the song lyrics as canonical, rather than events as they (amusingly) transpire in the video.

My problem with both of the above analyses is: they use game theory, rather than individual decision theory. Now at first this might seem crazy – isn’t it obvious that the situation involves (at least) two rational agents, with the outcome dependent on choices by both players? And such a situation is just the sort which should be dealt with using game theory rather than individual decision theory. Both of the linked to analyses seem to think to, as their approach is to outline what the optimum strategy for Carly is, given the payoff matrix they think the song describes.

The thing is, Call Me, Maybe doesn’t actually describe a payoff matrix at all. We get a fairly good idea about what Carly wants, it’s true. But here is all we know about the person being called: they are male (since other males are referred to as “other boys”), they are not particularly forthcoming with their feelings (they take a while to call, and then give “nothing at all”), they are prone to staring (“stare was holding”) and are scantily clad (“ripped jeans, skin was showin’”). This is not very much at all. It is certainly no basis for attributing a particular pay off matrix to the fellow.  The situation is worse than it just not being possible to give a determinate payoff matrix. It’s not actually obvious that the situation involves two rational agents at all. Carly self-describes her own actions as “crazy” even while performing them; all we know about the fellow’s behaviour is emotional aloofness and a penchant for long bouts of staring. Given the difficulties game theory runs into when dealing with non-rational agents, and given that we – both Carly nor the modellers – are operating under insufficient information to form a payoff matrix for the fellow, I submit that using game theory to model this interaction is the wrong way to go about it.

None of this, however, prevents modelling the situation decision theoretically. In fact I think there is a very simple model of the situation which would explain the logic of Carly’s actions and manage to explain some of the more obscure lines in the song. 

Although the circumstances are vague (don’t ask her, she’ll “never tell”; my guess is that it is a club which she has paid to enter – “pennies and dimes for a kiss”) Carly has met a man. She doesn’t have much information about the fellow (“I just met you”) but feels some attraction to him (“I took no time with the fall”), presumably based on his looks (“It’s hard to look right at you baby”). Given this, she considers exchanging contact details, and would prefer it if he called her back (“Here’s my number // Call me, maybe?”). However, alas, we all know that becoming romantically involved with handsome strangers is a risky business. So Carly must also consider – if I do interact with this person, will they turn out to be a total jerkface? Because if he is a jerkface, she’d rather they just didn’t get involved at all. The knowledge that she may end up involved with a jerkface is, I claim, is the reason for her expressing hesitancy (“Call me, maybe?”) 

Simplifying all the ways a person can be a jerkface into them being “not nice” we can create a table which makes clear the decision Carly faces:

Now, she needn’t consider the scenario where she doesn’t give him her number in order to make her decision. After all, if she chooses not to interact with this person, then it really doesn’t matter much to Carly what he is like, so the outcome is the same either way. So I take it she really only cares about his character if she actually does go ahead and give her number to this chap. Hence she need only consider the first row.

I make the assumption that the best and worst case scenarios are as good and bad as each other compared to meh scenario. In this case standard decision theory tells us that Carly's decision boils down to a simple question: is he more likely nice or not nice? If it is more likely that he is nice, then she is probably going to get the best case scenario out of giving him her number. If he is more likely horrid, then she is probably going to get the worst case scenario. So give her number if he seems nice, and don’t give her number if he doesn’t seem nice. 

We can thus make sense of the song, including some of its more obscure lines, if we see much of it as her deliberations on the matter. For instance, she frequently mentions her interactions with other men (“All the other boys try to chase me” is in the chorus). This, I claim, is Carly thinking about the frequency with which similar interactions with men have resulted in good vs bad outcomes. (On one interpretation of probability this is perhaps the only relevant thing to consider). Another line is about Carly doing all she can to gather information about the fellow (“I beg and borrow and steal”). She even explicitly mentions – and praises – her own ability to make judgements (“Have foresight and it’s real”). 

In the end she decides that, though it is crazy, she is going to give the fellow her number. Our last task will be to explain why she judges giving her number to the fellow to be crazy. I think we can rule out the possibility she decided that she has enough information to know the fellow is nice. If she knew that, giving him the number just wouldn’t be crazy.  So given that, there are two ways of interpreting the “This is crazy” line, depending on whether you think Carly is herself rational. 

The first, less charitable way of looking at it, is that after thinking about it, she comes to the decision that it is more likely the fellow is horrid than not horrid… and then still decides to give her his number, even knowing that. So she self-describes the action as “crazy” because she knows it is irrational. This might also explain why she has resorted to a life of crime (“I beg and borrow and steal”) – she is trying to impress somebody she believes to be a bad boy. Likewise it might explain why he is emotionally aloof (“You gave me nothing at all”) – one way of being a jerkface is to just not care about the person you are involved with.

However, I don’t like this way of looking at it. It presents Carly as irrational and I would prefer not to do that. There are philosophical issues about how we could possibly come to learn about Carly’s preferences in a way that would make sense of this. And, finally, she seems to be happy about his involvement in her life even in retrospect, and wants to express gratitude to him (“Before you came into my life I missed you so bad… and you should know that”). So I prefer a second, more charitable way of looking at it, which preserves Carly’s rationality.

The story one has to tell for the second interpretation is, I admit, a bit more complex. It goes as follows. Carly feels, for whatever reason, that she just has to make a decision on this immediately (that is why, I think, she frequently says that he is “in my way” – Carly means that this decision is facing her now). This renders it impossible to gather more information. Unfortunately she does not feel she has enough information at present to decide the matter. So, perhaps because she is applying the principle of indifference, she thinks it just as likely the man is nice as it is that he’s horrid. The two cases are equally likely, and in this scenario giving him the number is just as rational as not giving him her number. So she has taken a chance: as a result of some randomisation procedure she has chosen the optimistic over the pessimistic course of action, and handed over her number. Speaking loosely she describes this as “crazy”. Strictly speaking, it is a perfectly rational act given her information and desires, but there would be no pop-music potential in the chorus “Hey, I just met you // and this is a rationally permissible but non-obligatory action// here’s my number // so call me, maybe?” What is more, I think we can all understand her sense of excitement, as she makes her move here – she is taking a step into the unknown, taking a risk for the sakes of love after rational thinking had stopped being a useful guide. There is a certain romance to this, and thus I submit it a more fitting interpretation of the song.