Why Chess Tells us that Rationality is Impossible

February 7th, 2016

Defining rationality is challenging, but Nobel Prize-winning economist Herbert Simon has provided us with three ways to think about this important topic.

 

Substantive rationality concerns the degree to which a decision maximizes utility — or, from an evolutionary biology perspective, the degree to which it maximizes reproductive fitness. Evaluating substantive rationality requires a comparison between the content of a decision and the desired outcome. When economists speak of rationality, they’re usually referring to substantive rationality.

 

While substantive rationality is simple in concept, it’s nearly impossible to measure in practice. For example, we can’t quite answer the question that substantive rationality demands: “Given all the choices you could have made, was eating a banana the best one?” Still, substantive rationality is the logical theoretical yardstick for evaluating decisions.

 

In contrast, procedural rationality concerns the degree to which a decision is the outcome of a reasonable computational process. Procedural rationality requires consistency and coherence of preferences and choices. For example, a choice that is procedurally rational should abide by transitivity: if I prefer bananas to apples, and apples to oranges, then I should prefer bananas to oranges.  

 

Economists generally ignore procedural rationality and assume that we'll abide by procedural axioms, such as transitivity. However, decades of research tells us that we break the fundamental rules that underlie procedural rationality: we resort to heuristics, fall prey to biases, and exhibit inconsistent preferences. As a result, psychologists are acutely interested in procedural rationality as a benchmark against which we can measure our systematic decision biases. 

 

It's important to realize that our inability to abide by procedural rationality isn't the only roadblock to substantive rationality. Even if we could achieve procedural rationality, the option space is often so vast that we cannot make an optimal decision — i.e., it is computationally intractable. For example, there are about 10120 possible combinations in a chess game, which is many times larger than the number of atoms in the universe. With this understanding, we arrive at Simon’s concept of bounded rationality, which is defined as maximizing within the constraints of limited knowledge, limited time, and limited cognitive processing power.  

 

While no specific criteria exist to determine whether a decision is boundedly rational, it’s a helpful concept that frees us from the unattainable and unhelpful standards derived from neoclassical economics. Most importantly, it reminds us that when we discover departures from procedural rationality, we shouldn’t sound the alarm bells and decry the foibles of the mind. Sometimes we simply reach the limits of the universe.