Model: Build Habits with Self-Love

This is the first in a series of posts I'm calling "Models," which will expand, develop and apply the tools of the social sciences as a way of thinking about our own lives.

First, a story.

The Setup

Alexis is a lot like any other young woman. She works as a recruiter at a growing tech company. It's a high pressure job, because the market for top talent is highly competitive, but one she enjoys. Every other weekend she visits her boyfriend, who lives a couple hours away, but with little time together, they try to pack in as much fun as possible.

Between the hectic job and the busy weekends, she pretty much always feels harried.

One day she finds a rash on the top of her left foot. She wears shoes that cover the rash until she can get to a doctor, who gives her a cream to put on it and tells her she's not exercising enough.

"But I walk to the office from my car every morning and back every evening!" she complains.

"I wouldn't count that as exercise," the doctor says, unmoved.

"Hmm. Well why does exercise matter so much, anyway?" asks Alexis.

"It just does," says the doctor. "Click on that link if you want to learn more. Try to exercise for 30 minutes every day."

Alexis leaves the doctor's office and resolves to start exercising today, as soon as she gets her foot cream. After all, if exercising is good for her, then the utility of exercising must be positive:$$u(e) > 0$$, where $u$ is the utility function (think of it as the subjective value/joy/goodness of something) and $e$ is the action of exercising. That it's greater than $0$ implies that Alexis thinks the benefits of exercising outweigh the costs. (See appendix at bottom of article for variable reference.)

Pumped up to get healthy, Alexis goes to the gym and starts pumping iron. This is harder than Alexis expected. Three sets of squats in, she realizes that maybe $$u(e) < 0$$, since lifting weights hurts and she will have to do it like a gazillion more times before it will have any effect on her health.

The Model

Obviously the utility function is a little more complicated: $$U(e,r) = u(e) + u(r)$$, where $U$ is the total utility of exercising regularly, and $r$ is the action of continuing to exercise in the future. \(u(r)>0\), massively so, in fact, so $u(r) > |u(e)|$. This implies $U(e,r) > 0$ despite $u(e) < 0$.

Why, then, does Alexis have such a hard time getting herself to exercise? The answer is obvious from the formula. Exercising now hurts, and has no effect on whether she will continue to exercise in the future, which is really the only thing that matters. The health benefits of exercising once are negligible. So all Alexis has to do is never exercise today but always exercise tomorrow, and she's swimming in gravy.

Unfortunately, she can't make decisions for her future self. She has no control over $r$.

This problem is further compounded by what economists call present bias, the idea that we care much more about today than tomorrow. Not only does Alexis lack control over her future behavior, but she doesn't even care about her future self as much as her present self. This is modeled with a coefficient, $\beta$, applied to all future utilities. This gives us $$U(e,r) = u(e) + \beta u(r),$$ where $0 \leq \beta \leq 1$. However easy it was for the doctor to tell Alexis to exercise more, her actually exercising more is getting less and less likely as we develop the model.

While we're introducing $\beta$, let's add it to the other place where it belongs. $u(e)$, as I mentioned, represents a cost-benefit analysis and Alexis incurs the costs of exercising in the present while enjoying the benefits of exercising in the future. That gives us $$u(e) = C(e) + \beta B(e).$$ The last obstacle Alexis faces is the uncertainty of $r$ occurring, since it is out of her power. That uncertainty is represented in our formula through probability $p$, which like $\beta$, is between 0 and 1.

Finally, we have a formula that shows why it's so hard for people to exercise: $$U(e,r) = C(e) + \beta B(e) + p \beta u(r)$$ At the time when Alexis is deciding whether or not to exercise, the benefits of exercising are wanly felt while the costs are felt at full force.

StackOverflowError no more!

Now, I didn't just bring you here to tell you why its hopeless trying to get yourself to exercise. I firmly believe that building and understanding models of our behavior gives us a power to leverage pressure points in those models.

Take a moment to analyze the model and see how you can turn it to your advantage. The important thing to note here is that Alexis is stuck in a loop. $p$ is actually a function of $U$, whereby the more utility Alexis gets from exercising, the more likely she is to exercise going forward. The good news is that Alexis wants to be in a loop. She just wants to be in a good one.

I call solutions to such loop problems break points because we're trying to break out of a loop. In this particular case, a break point done right can automatically put Alexis in a positive loop, where both $p$ and $U$ will have high values.

How can we break Alexis out?

I see a few options. Let's start with the simplest. Alexis can try to make exercise fun for herself. Instead of lifting weights, Alexis could do something she'd want to do anyway, like dance or rock climbing or soccer. That would introduce another $B_n(e)$, but this one unmodified by $\beta$, so long as fun happens in the present. Once $u(e) > 0$, the problem is solved and Alexis is in a positive loop. In this case, the model becomes:$$U(e,r)=C(e) + B_n(e) + \beta B(e) + p \beta u(r)$$ Unfortunately, our model applies to more than just exercise, and it's not possible to make everything fun all the time. Realistically, you're going to have to eat a shit sandwich now and then. A good loop with bad break points is a bad loop.

Alexis $\heartsuit$ Alexis

Now we get to the point I promised in the title of this post: you can break out of the loop with self-love and self-trust.

Alexis, for the moment, is stressed out by work and lonely because her boyfriend lives hours away. She has trouble keeping up with the other recruiters at her firm, despite working late, and at the end of the day she comes home to her studio apartment exhausted. She likes the work, but she doesn't know if she has what it takes to be successful. Whenever she screws something up, she can't help but berate herself.

How is she ever going to move up in the company if she can only make two new hires a month? All the other recruiters seem to make four or five hires a month, and all of those new hires seems better than the talent she pulls in. What's wrong with her? After acing high school and going to a great university, why can't she cut it here?

Alexis is starting to give up. She's not depressed, exactly, but when she's deciding whether to go exercise, she does wonder, what's the point?

In effect, this lowers $u(r)$, but the opposite paradigm (viz. self-love) not only raises $u(r)$, but throws in another friendly $B_n(e)$ for all actions that raise $u(r)$.

Think of it this way. If Alexis feels the way about herself the way her mother feels about her, with pure, constant love, Alexis will feel really good about doing things for herself. Every time she goes out and exercises, even if it's hard and unpleasant, she will feel really good about taking care of herself.

A similar effect is in play if Alexis can learn to trust herself. The more times Alexis says she is going to do something and then in fact does do it, the higher $p$ becomes. Combined with raising $u(e)$ by adding in $B_n(e)$, raising $p$ makes exercise start to look pretty damn attractive.

Applying the model

How can Alexis put this into practice?

Building self-love is tricky, but not as tricky as building economic models. Alexis starts by complimenting herself anytime she does something well or does something for her future self, no matter how small. If she gets to work on time, way to go Alexis! If she has a piece of fruit with breakfast, you rock Alexis! The bar should be pretty low. Love does not need to be earned. It is freely given.

Then Alexis walks the walk, not just complimenting herself but actually doing things for herself. She makes sure she stays hydrated. She takes the stairs at work. She goes to sleep early. All easy things, and all done out of love for herself. Then she starts doing things that are a bit more challenging, but she loves herself, so it makes total sense to do it.

Building self-trust isn't tricky at all. All Alexis does is commit to doing tiny, easy things and then does them. She says to herself, "I'm going to drink water when I wake up in the morning." When she wakes up in the morning, she drinks some water. She tells herself, "I'm going to read a page of my book when I lay down tonight." When she goes to bed, she reads a page of her book. Simple. Before she knows it, she can tell herself to do things and be confident she will do it.

By loving yourself and finding immediate value in self-care, you, too, can fight your natural tendency to undervalue your future well-being. By establishing self-trust, you can demolish the uncertainty of your future self's behavior and move forward with confidence.


$u(x)$: utility function
$e$: the action of going out and exercising
$r$: the long-term behavior of exercising regularly
$U$: multi-period utility function $\beta$: coefficient of present bias, always between 0 and 1
$C(x)$: immediate cost of x
$B(x)$: future benefit of x
$p$: coefficient of uncertainty, always between 0 and 1
$B_n(x)$: immediate benefit of x