On Risk and Uncertainty: the Ellsberg Paradox, Goats, and my friend Yoav

Last week, I had lunch with Yoav, one of my first friends here at Harvard Business School. As it happened, we got lucky and were seated next to each other on the very first day of class, and from then on, took every class together for the first few months.

Over Spangler’s juicy chicken thighs – it was Friday, after all, which called for a celebration – we found ourselves talking about risk and uncertainty. I had to fill him in on what I had just learned in class.

The Ellsberg Paradox

In 1921, economist Frank Knight drew a distinction between risk and uncertainty. He defined risk as a situation where the outcome is unknown, but the set of potential outcomes and their probability distribution are known. In risky situations, people then make decisions maximizing their expected utility. In uncertain situations, however, Knight argued that neither the outcome nor the underlying probabilities were known. Thus, people are not able to make fully rational decisions.

In 1954, mathematician Leonard Savage countered that, in the absence of a probability distribution, humans infer probabilities and make decisions based on those assumptions. He called this subjective expected utility.

Enter Daniel Ellsberg, the protagonist of this story. In the early 1960s, he devised an experiment that he sent to the leading economists of his time to investigate this.

The Experiment

An urn contains 90 balls. Thirty of them are red, and the remaining 60 balls are either black or yellow in unknown proportions. Thirty balls in total will be drawn.

Would you rather:

• A: Receive $100 for each red ball drawn, or

• B: Receive $100 for each black ball drawn?

Now, mark down your answer. Then, would you rather:

• C: Receive $100 for each red or yellow ball drawn, or

• D: Receive $100 for each black or yellow ball drawn?

In our classroom, approximately 70% chose A over B, and nearly 90% chose D over C. This pattern was consistent with Ellsberg’s findings in the 1960s among the world’s leading economists (as opposed to mere business school students). Importantly, the results contradicted Savage’s subjective expected utility theory.

If you chose A over B, you implicitly assumed that there are fewer black balls in the urn than yellow ones – or that they are equally numerous. Given that assumption, a rational decision-maker maximizing their utility would then choose C over D, since we just established there are more yellow balls than black (or if you assumed they were equal in number, you shouldn’t have a preference). However, as seen in our classroom votes and in Ellsberg’s findings, people overwhelmingly prefer D over C.

The Ellsberg Paradox disproved Savage’s subjective expected utility theory: Rather than inferring a probability distribution and maximizing their expected utility when faced with uncertainty, people seem to shy away from ambiguity.

Goats

One of the great things about Yoav is that he doesn’t just listen to and get me, but actively adds relevant points to the conversation. So, he told me about the Monty Hall Problem, where you try to choose the right door to win a car: there’s a car behind one of the three doors, and a goat behind each of the other two. For the sake of brevity, I’m just linking it here. The point of the problem is that we are not very intuitive when it comes to statistics.

Actually, psychologist and Nobel laureate Daniel Kahneman makes a similar argument in Thinking, Fast and Slow. He explains that while people have a strong, automatic intuition for grammar – native speakers, for example, can immediately sense when a sentence is grammatically incorrect even if they cannot articulate the exact rule being violated – the intuition does not extend to statistics. Humans are outright bad at intuitive statistical reasoning.

Back to the chicken thighs

All of this led Yoav and me to reflect on the risks – or rather, uncertainties – that we may be miscalculating at the moment. For many of us graduating students, career choices are top of mind; specifically, the decision between a salaried job and an entrepreneurial path.

Taking a salaried job, one could argue, is akin to Ellsberg’s option A: it offers a known but, importantly, average outcome. Opting for entrepreneurship instead means accepting the risk of falling below that average, while also opening the door to significant upside – that is, option B. As we’ve seen, the natural human tendency is to shy away from ambiguity, even when the expected outcomes are the same in both cases.

Perhaps an even more compelling argument is that many of us don’t actually face a real downside with entrepreneurship. With a good education and professional background, the worst-case scenario is simply a delayed acceptance of a salaried job, offset by the valuable lessons gained from a failed business. More broadly, at least in my native Finland and other Nordic countries, government-provided unemployment insurance, universal healthcare, and other social benefits help mitigate the downside for everyone – not just those who have chosen and been able to invest the time and money in a prestigious education. So, while uncertainty remains in entrepreneurship, the expected utility may well be higher.

I’m challenging myself, Yoav, and all of us to reassess the uncertainties in our lives that we may currently be miscalculating or avoiding in fear of ambiguity. Instead of focusing on the downside, perhaps the right question to ask is: are you willing to walk away from the chance of doing exceptionally well?

/ Ss

Me and Yoav, friends and seat mates

P.s. The (first two) pictures in this post are created with Recraft, a new AI-tool my friend Annabel introduced me to last week

P.p.s. If you thought this was cool, subscribe below for the free (and for the time being, sporadic) newsletter