How do we become Super-Rational?

Lessons from a Beauty Contest

A version of this article appears in my book, Twisted Logic: Puzzles, Paradoxes, and Big Questions (Chapman and Hall/CRC Press, 2024).

THE NUMBER DILEMMA

In the Number Dilemma, participants must choose a whole number between 0 and 100, aiming to get closest to two-thirds of the average number chosen by all participants. This scenario tests not only numerical reasoning but also understanding of human behaviour.

LEVEL 1 RATIONALITY: CHALLENGING THE AVERAGE

If you were to assume that the other participants would choose a random number within the given range, the average number chosen by everyone would be 50. Under this assumption, you might believe that choosing 33, the nearest integer to two-thirds of 50, would provide a high probability of winning. This initial strategy, known as Level 1 rationality, might appear intuitively logical.

LEVEL 2 RATIONALITY: ANTICIPATING THE AVERAGE OF THE AVERAGE

However, upon closer inspection, a new insight emerges. Since you reasoned that choosing 33 was a smart move, it is reasonable to assume that other participants will arrive at the same conclusion. Consequently, the average number chosen by all participants would shift towards 33. To maximise your chances of winning, you decide to adopt Level 2 rationality and choose a number lower than 33. In this case, 22 appears to be the optimal choice.

LEVEL 3 RATIONALITY: GOING DEEPER INTO ANTICIPATION

As you delve deeper into the rationality levels, a pattern begins to emerge. Just as you contemplated that others might select 22, they too will likely adopt the same line of reasoning. To outsmart them, you employ Level 3 rationality and opt for the number 15. The idea is to anticipate the choices of others and select a number that is two-thirds of the average they might choose.

LEVELS OF RATIONALITY

In summary, the levels of rationality illustrate the iterative process of outthinking others.

APPROACHING ZERO: THE ULTIMATE RATIONAL CHOICE

As you progress through each level of rationality, however, you cannot help but notice a concerning trend. As rationality levels increase, choices converge towards zero, posing a paradox: Is zero really the most rational choice when considering human diversity in decision-making? Deep down, you begin to question the effectiveness of choosing zero.

ACCOUNTING FOR DIFFERENT LEVELS OF RATIONALITY

Your uncertainty arises from the realisation that not all participants are likely to think or reason in the same way. Variations in human rationality mean that some may choose randomly or with less strategic depth, affecting the overall average and optimal choice.

THE WINNING NUMBER

In a practical application of this dilemma involving Financial Times readers, the winning number was 13, showcasing the unpredictability of collective rationality.

KEYNESIAN BEAUTY CONTEST IN FINANCIAL MARKETS

The economist John Maynard Keynes encapsulated the essence of the dilemma in his work, ‘General Theory of Employment, Interest, and Money’. He likened professional investment to a newspaper competition where participants must select the prettiest faces from a selection of photographs. The prize is awarded to the competitor whose choices align most closely with the average choice of all participants.

OUTGUESSING THE BEST GUESSES

Keynes emphasised that participants should not merely choose what they believe to be the prettiest faces according to their own judgment or average public opinion. Instead, they should anticipate what average opinion expects the average opinion to be. In essence, winning the competition relies on outguessing the best guesses of others—a strategy referred to as super-rationality. Just as in the Number Dilemma, the Keynesian Beauty Contest involves predicting others’ predictions, a strategy crucial in financial markets and investment decisions.

DISCOVERING THE HIDDEN OPPORTUNITIES

In the context of this so-called Keynesian Beauty Contest, the concept of super-rationality holds tremendous significance. This strategy involves outthinking the crowd’s average opinion, a concept that can reveal overlooked opportunities in various contexts. By transcending the common line of reasoning and adopting a super-rational approach, individuals can unveil hidden possibilities and potentially reap rewards. While these concepts offer intriguing insights, their practical application is complex due to the unpredictable nature of human decision-making and diverse levels of rationality.

CONCLUSION: EMBRACING SUPER-RATIONALITY

The Keynesian Beauty Contest serves as a captivating thought experiment that challenges traditional notions of rational decision-making. It showcases the complexities of human behaviour and highlights the importance of anticipating the actions of others. By embracing the concept of super-rationality and outguessing the best guesses of the crowd, individuals can navigate these intricacies and increase their chances of success.