# Reason cast in equations

Casting the rational behaviour of individuals in mathematical models and learning from these for use in reality: Daniel Rehsmann recently completed his doctorate in microeconomics and, among other things, he explored the conditions under which it is rational to spread misinformation.

“The beauty of mathematics is that we can define reason with three equations that can be applied to most interactions between people,” says Daniel Rehsmann. In contrast, Immanuel Kant required around 700 pages for his ‘Critique of Pure Reason’. Daniel Rehsmann elaborates: “It is possible to describe everything that an individual desires and that justifies their decision in mathematical terms. The desires and needs of individuals are often contradictory, and in modern microeconomics we use the term equilibrium to describe the result of their actions”, Daniel Rehsmann goes on to explain.

We ask whether individuals always behave rationally and whether their behaviour can therefore be easily cast in mathematical models. Daniel Rehsmann points to the cocoa the editor is currently sipping and explains: “Most of the time it’s that simple. If you prefer cocoa to coffee, you will order a cocoa. If you prefer cocoa to coffee, and coffee to tea, we can conclude that you probably also prefer cocoa to tea. If you act accordingly, your behaviour is mathematically rational.”

Daniel Rehsmann sees himself as an applied economist. His primary interest does not lie in mathematical properties, but in actual interactions between individuals, which he finds intriguing and which present a challenge when it comes to translating them into mathematical models. He offers an example: “Since Donald Trump’s election as US president, I have been thinking about the conditions under which it is rational to spread misinformation.” This question turned into one of three projects in his doctoral studies. He started by taking a close look at reality and rigorously recording his assumptions on paper: “A further advantage of mathematics is that it forces us to formulate our assumptions very precisely. Modelling also means simplification.” This model is subsequently tested on countless examples until, in the end, we gain insights into the equilibrium in these interactions.

And what has Daniel Rehsmann learnt about the individuals who spread misinformation? “Let’s take two companies that manufacture products with different quality grades. Intuitively, we assume that it is rational for a low-quality company to spread misinformation in order to give its consumers a false impression of its quality. At the same time, companies also benefit from differentiation. Our model weighs up these effects: A key result of our analysis is that the difference in the qualities of such products must be sufficiently large to make the dissemination of misinformation rational in the first place,” the researcher concludes.

The method used by Daniel Rehsmann is called game theory. The necessary tools for this are mainly found in mathematics, which the graduate of the Master’s degree programme in Business Administration had to acquire before embarking on his doctoral project. Today he knows: “If I had to start again, I would study mathematics.” He has now completed his doctoral thesis under the supervision of Paul Schweinzer (Department of Economics). At the same time, he has been and continues to be involved in a research project for the University of Vienna. Daniel Rehsmann believes in basic research: “Knowledge in itself serves its own purpose. I refuse to view science merely as a supply service for the economy.” His next career steps are not yet set in stone. One thing is clear: “Financial security is all well and good, but if I have to choose, I’ll opt for the intellectual challenge.”

## A few words with … Daniel Rehsmann

What would you be doing today if you hadn’t chosen to work as a scientist?
Actor or photographer.

Do your parents understand the things you are working on?
Probably not fully, unfortunately.

What is the first thing you do in the office each morning?
As nerdy as this may sound: a software update.

What makes you furious?
Racism.

What calms you down?
A good novel.