There is an Austrian saying that “happiness is a bird” (“Das Glück is a Vogerl”). The idea, I think, is that happiness is hard to catch and even harder to keep hold of. In this blog post, I want to offer a formal model and definition of happiness that is able to generate the fleeting nature of happiness.

First, a bit of casual introspection to set the stage for modeling ideas. Imagine that sometime around early winter you finalize your summer holiday plans. You are planning a road trip through Australia (in their winter and your summer), something you are very excited about. Imagine that a month later – still (your) winter – you learn that something happened that is not a big problem in itself, but that will prevent you from going to Australia after all. Say, it turns out you can’t take that particular time off after all, but that is the only time that would have worked for the other people you were planning to go with on this trip. You will probably be very unhappy. And you will be unhappy right then and there, in (your) winter, months before you were supposed to be going on this trip. You don’t wait to be unhappy until the summer comes along. In fact, when the summer does come along, you will probably already be less unhappy, you have already “worked through” your grief.

The key element that I want to take up from this casual introspection is that humans are very forward-looking. They create expectations of the future and, in a sense, “consume” at least part of their future expectations before these are realized. And, as I will argue, humans who are good at forming correct expectations will likely only be happy for short amounts of time. They will not be able to live in a permanent state of bliss. [On the flip side they will also only be unhappy for short amounts of time.]

One way to see things is that there are many possible paths that your life could take. You control some aspects of which path you get, but no matter how much you control things, how much you “take life into your own hands,” there is always some leftover uncertainty. In fact, there is probably a lot of leftover uncertainty. You make educational choices, you decide what to study, and you decide which jobs you apply for, but what job you end up getting and where is not only up to you. You make friends and have a family, but who exactly they are and what happens to them, something you also care about, is again not all down to you.

Turning to a mathematical description of your life, we can collect all possible paths of life that could happen to you in one big set At the beginning of your life, you have a belief about the likelihood of these various possible paths, which we capture by a probability distribution over Ok, you probably have to grow up a bit before your beliefs form, but, at some point, you will probably have one. And yes, you might not exactly be able to write it down and articulate it fully, and maybe you have a more diffuse notion of your future that you don’t feel you can capture by a probability distribution, but I think you will see that this is a useful notion. The next ingredient to studying your happiness is to consider how much you would value different paths of life Here, I am not sure whether what I propose is the best way to model this – I am following standard models of intertemporal choice in economics and I haven’t thought deeply enough about possibly better alternatives. The idea is that a path in life gives you a level of instantaneous satisfaction at any moment of time I will, for simplicity, count time discretely in, say, days. A path would then give you a sequence of instantaneous levels of satisfaction for all days, from day zero (now) until the end of days. Call these levels of satisfaction I am using because in economic models this is what you often see, with for utility. As people are forward-looking at any time they care not only about the time-t instantaneous level of satisfaction but also about those in the future. A nice and simple way to capture this idea is that you do what firms are supposed to do when they consider long-term investment decisions: you compute the net present value of, in your case, all your future levels of instantaneous satisfaction. Each path of life for every moment of your life then yields a time-t lifetime satisfaction, let’s call it for some discount factor Note that you can potentially live forever here. However, we can interpret the so-called discount factor as at least partly reflecting your less-than-certain chance of surviving until the next day. In that case, even if you could live forever in theory, the chances of that happening are zero. The discount factor can partly also reflect your degree of impatience.

So, we have formalized the possible paths of life and their consequences for us in terms of lifetime satisfaction. I have not yet mentioned happiness. And happiness will not be the same as lifetime satisfaction. I guess this is a bit controversial, but I believe that happiness is what we experience when things turn out better than expected. And we are unhappy when things turn out worse than we expected. To capture this, we introduce events – things that can happen to us. One way to see this is that, as time goes on, we can rule out more and more paths in life. This can be captured by a stochastic process that is a filtration. It has the property that whatever you know to be true at time you also know to be true at time for all You don’t forget and you may learn new things. Suppose we call the information (about your path in life) that you have received up to and including time

I can now finally define your happiness as the difference between your “updated” expected time-t lifetime satisfaction and your “original” expected time-t lifetime satisfaction. Formally, happiness is given by I should probably cite some literature now that justifies my definition of happiness.  The best I can do is to point you to the work of Arthur Robson on the biological basis of human (economic) behavior. I am not sure he would quite agree with my model here, but it is partly based on my, possibly imperfect, reading of his work. I came to the belief that happiness is not the same as lifetime satisfaction and that mother nature uses our pursuit of happiness (through the clever use of short-lived dopamine bursts) not to make us happy but to make us always want to achieve more and more and more – ever to increase our evolutionary fitness. Given mother nature’s biological constraints, she chose to make happiness have less to do with the level of lifetime satisfaction but with how it changes when certain events happen to you.

If happiness is given like this, continued happiness (undermining mother nature’s goals) would be best achieved by maintaining low expectations. Sage advice I would think, but hard to follow. Ideally, you would never expect a good meal and always be surprised when you get one. “Oh boy, I am getting something nice for breakfast!” This is difficult to keep up when you get a good breakfast every day. But it would quite possibly be a happier life.

When I lived in Chicago, I flew back to Austria to see family about twice a year. I collected air miles and fairly soon had a good stash thereof. I don’t know if it was a glitch in the airline’s system, but when just before boarding I asked for an upgrade based on my air miles, I often got one without the airline ever taking any miles off my account. I kept getting upgraded. The first time this happened to me I was extremely happy. It was one of the best flight experiences I ever had. This is so, I believe, because it came as a surprise – I did not expect to be upgraded. But after a while, the experience became more routine and did not give me that much happiness. I came to expect an upgrade. When I then did not get one, I was pretty unhappy. I was, in fact, much less happy than in the earlier days when I was never upgraded and never expected to be upgraded.

My kids form high expectations almost too easily. We had ice cream after lunch one Friday, and happened to have ice cream after lunch on the following Friday as well. When the kids didn’t get ice cream after lunch on the next Friday, they were unhappy and were asking us “what happened to Friday ice cream?”

Of course, I have described only one aspect of happiness. I am, for instance, ignoring things like clinical depression, which I would find harder to model and even harder to explain. I am also ignoring happiness that stems from achieving something. For instance, I would value the view on a mountain peak very differently depending on how I got to this peak. I believe I would get much more “out of” the view at the peak if it came as a reward at the end of a long and challenging hike rather than being the result of being dropped off by a helicopter. All I wanted to offer in this post was a formal model that can generate the fleeting nature of happiness, at least as I perceive it. But there is a lot more that could be said about the strange nature of human happiness.