The rationality paradox

Dog-Eat-Dog by Ruth Graham

There are important differences between humans and other animals, and we should account for them when trying to model their respective behaviours. One difference is that humans can understand mathematical models, while there is no known example of this in animals.

In economics, the Lucas critique is a useful piece of advice about modelling human behaviour. It alerts us to the fact that if people are aware of the model we are using to predict their behaviour, they can adjust their behaviour to exploit our naivety. Even if they don’t know the exact model we are using, if we have not accounted for their strategic behaviour, they can still take advantage of us.

One paradox about the Lucas critique goes as follows. Lets take the classic example of a model, called the Philip’s curve, used by central bank managers to set inflation and try to reduce unemployment. This model is subject to exploitation by rational firms who can manipulate their employment patterns given that they know the inflation strategy of the bankers. As a result, the Philip’s curve will fail to make a correct prediction and is thus subject to the Lucas critique.

This is a reasonable observation, but why are the firms assumed to be rational and the central bank managers irrational? Surely, these highly qualified, trained economists would have thought of this possibility and incorporated the reaction of the firms into their model? This is all the more surprising when you consider that firms have many other things to think about than inflation five years in to the future. Apparently, on top of all their immediate concerns about their business model, staffing problems etc. these firms have dedicated their time to finding loopholes in the central bank’s thinking.  Why should the bankers (apart from Lucas, of course) have missed this fact, while the firms are able to work it out?

Any Lucas-inspired model of these bankers behaviour should not allow them to use the Philip’s curve in the first place. The only logical conclusion of this line of reasoning is either that the observations of the economists using Philip’s curves was mistaken or it was some temporary insanity which is replaced by a steady state rationality in the future.  

When we build a mathematical model of human behaviour, the Lucas critique should be taken seriously. Understood properly, it says you should think a few steps ahead when making your model. Does your model make sense? Lucas was pointing out that the Philip’s curve model has a particular type of limitation. We should remember this limitation when we are building models. The Lucas critique is one of many such limitations.

But the paradox tells us that the Lucas critque should not be taken too seriously either. Taken to an extreme, the critique says that the only thing economic models should be used for is studying the outcome of rational interactions. If this were the case, then the paradoxical question is why economics exists at all? The rationality assumption is that people are able to work out the consequences of their actions and therefore we don’t need an economist or anyone else presenting them with a model of what those consequences might be.

This description is typical of paradoxes in mathematics where we want to say something about a model using the model itself to say it. Last month I wrote a blog post about Bertrand Russell spending 20 years doing this to no avail in trying to establish the axioms of mathematics.  It just isn’t possible.

I was prompted to write this after a blog post by Simon Wren-Lewis that Richard Mann tweeted me. Although I find scathing attacks on economics amusing, I find it difficult to believe that economists or anyone else takes the Lucas critique as far as appears to be claimed.  This would be completely irrational. I also doubt whether, as is also claimed, that we can really attribute the economic crisis to models based on rationality.  But it is certainly fun thinking about it.

Positive online emotions

Emotions and mathematical models are perhaps polar opposites. Emotions consist of personal opinions, they are unlikely to be rational and they can change in a second. Mathematical models are logical, rational, descriptions of the world that are meant to stand the test of time. But that doesn't mean that we can't model emotions, or at least this is was what Frank Schweitzer claimed in his seminar at the Futures Institute last Friday. Before Frank's talk I was a bit skeptical, but I was interested to find out if he could really build an emotional model.

In order to model something, you first need to measure it. You need to be able to assign a number to an emotion. Since emotions are already either positive or negative, we already have a natural way to assign them values. Most of us can read a text and agree on whether it has a positive or negative tone. But can we automatically assign a number to emotional content on the basis of this assessment? Frank and his colleagues have adapted the software SentiStrength, which claims to be an algorithm to do exactly this. You feed it in a sentence and out pops a ranking. I put in the last sentence of the previous paragraph in to the online version and got negative score -2 for the words 'skeptical' and 'emotional' along with a positive score of 2 for 'interested'. Good to see I was emotionally neutral going in to the seminar.

Review sentiment distribution for
 'Harry Potter and The Deathly Hollows'

In one study, Garcia & Schweitzer looked at book reviews left on the Amazon website. There was a typical distribution of negative and positive emotions in these reviews (pictured on the right) where positive comments were typically extremely positive and negative criticism was varied. The time pattern of review writing varied, with some books building up a review base over time and others (such as Harry Potter) being hyped from the start.

Things get even more interesting when Frank and his colleagues looked at online chat rooms. They examined how long it took between interactions and whether the reactions were positive or negative.  They found a common distribution for the times between posts, which was independent of the topic. They concluded that people were surprisingly positive in their online interactions, even though previous studies had suggested that discussion is generated by negative opposing opinions. When online, people spend a lot of time being nice to each other! Not just pressing the like button, but also in constructive agreement.

Time series of emotions in
an online chat room. 

The team have built up a mathematical model of emotions, which they use to explain the patterns they see. The basic idea of the model is that people change both in how aroused they are and in whether they feel positive or negative emotions. Positive inputs provide positive expressions, while negative inputs enforce negative expressions. The arousal depends on the intensity of the inputs. This model can reproduce many of the properties of the Amazon data and the online chat rooms.

In another part of their work, Frank and his colleagues argue that “positive words carry less information than negative words”, so I better be a bit critical.  In the presentation, and the papers I have looked at since, I think a model comparison to the dynamics of the conversations and exchanges is missing. The model proposed captures the rate at which people comment and the positive/negative content of what they say. But the comparison to data is mainly at the level of time between posts or overall distribution of sentiment, rather than looking at the positive/negative interactions. I would like to see something down the lines of James Murray and co-workers on the Mathematics of Marriage. Here there is a description of how couples get in to negative/positive spirals and  predictions to how this bodes for the futures of the relationships of the couples involved. Murray’s work lacks thorough validation against data, and maybe it becomes too complicated once the fast amount of chat room data is put in to a model, but I would like to see more of these interaction dynamics. Maybe this is in some of the work and I have just missed it? Or maybe it is just too difficult at present? But I would be interested to see what can be done.