Choosing when you cannot know

Two kinds of not knowing

Decision researchers separate two situations that feel similar but call for different habits.

Decision under risk

You know the possible outcomes and their odds. A coin toss, a lottery ticket with published odds, an exam where you know half the marks come from one topic. The work is to weigh the options sensibly.

Decision under uncertainty

You do not know the odds, or even all the outcomes, and have to learn them by trying things. A new market, a new manager, an unfamiliar card deck. The work is to learn fast enough, and to weigh what you have learned.

The difference changes behaviour. In a review of three experimental set-ups, Ralph Hertwig and Ido Erev found that when people learn about options from experience rather than from a written description, rare events have less impact on their choices than their real probability deserves. Read about a 1-in-10 disaster and you may overweight it. Live through nine quiet rounds and you tend to forget it is coming. This is called the description–experience gap, and it matters for every game on this shelf, because all four teach you the odds through experience, one outcome at a time.

Tool one: expected value

The first question to ask of any risky option is what it pays on average if you could take it many times. That average is its expected value: multiply each outcome by its probability and add them up.

Expected value is the right yardstick when you face the same kind of choice many times and no single loss can knock you out. That describes all four of our decision games: each session is a long run of small choices, and your score is how much value you captured over the whole run. It is also why a candidate who takes the occasional sensible risk tends to finish ahead of one who never does.

It is not the whole story, for two reasons. First, averages hide spread. If losing 200 would end the game for you, the average is irrelevant and caution is rational. Second, people do not feel gains and losses equally.

Loss aversion explains a lot of behaviour you will meet on this shelf. It is why people bank a balloon too early after one burst, reject a lopsided offer that would still have paid them something, and abandon a good deck after one painful card. None of that is stupid. It is simply costly when the task rewards the long-run average.

• Expected return
• Chance of losing it all

Tool two: learning from feedback

When the odds are unknown, you have to estimate them from outcomes. The best-studied account of how brains and machines do this is the prediction error: after each outcome, compare what happened with what you expected, and move your expectation part of the way toward the result.

Written as a rule: new expectation = old expectation + learning rate × (outcome − old expectation). Suppose you expect a deck to pay about 50 per card, it hands you a net −200, and your learning rate is 0.2. The prediction error is −250, so your expectation drops by 50, to 0. A higher learning rate reacts faster but is thrown about by noise; a lower one is steadier but slow to notice real change. Our Card Decision report fits exactly this rule to your choices and shows the learning rate that best describes you.

This is not just a convenient model. Schultz, Dayan and Montague showed that dopamine neurons in monkeys fire in a pattern that matches a prediction error: a burst for an unexpected reward, no change for a predicted one, and a dip when a predicted reward fails to arrive.

Learning brings its own dilemma. To learn which option is best you must try the others (explore), but every try of a worse option costs you (exploit means taking the best-known one). In a study using slot-machine-style choices, Daw and colleagues found people switch between these two modes. Wilson and colleagues then showed that people explore more when they have more choices left to benefit from what they learn. That is exactly the right instinct: exploration is an investment, and investments pay only if there is time to collect.

Other people change the maths

Half of this shelf involves a counterpart. Once another person (or a simulated one) controls part of the outcome, the odds depend on their intentions, and their intentions may depend on how you treat them.

Classic economic theory predicted that self-interested people would never trust or reward trust in one-shot anonymous exchanges. Decades of experiments say otherwise: in a review of trust-game research, Alós-Ferrer and Farolfi note that real people are far more trusting and more trustworthy in the laboratory than selfishness would imply. People also punish unfairness at a cost to themselves. The practical skill is not to be trusting or suspicious by nature, but to read behaviour and adjust: invest where it is repaid, protect yourself where it is not, and remember that some relationships reward patience.

Three skills, four games

Our taxonomy splits decision making into three facets. The weights show how much each game contributes to your Decision Making score, which in turn is 15 per cent of your overall profile.

A useful way to hold the three together: all of them are about matching your behaviour to the evidence. Learning from feedback asks whether you notice what the evidence says. Risk calibration asks whether you act on it with the right boldness. Negotiation and trust asks whether you can read evidence that comes from another mind, and whether your own actions change what that mind does next.

Where you already use it

• Everyday: deciding whether to keep waiting for a late bus or book a cab; choosing which of two coaching institutes to trust after a demo class; how many practice tests to take before you stop and revise.
• Campus: which companies to apply to when you can only sit a few drives; whether to accept an early offer or hold out for a later one; how much of a group project to take on when you are not sure a teammate will deliver.
• Workplace: a new analyst testing three data sources and settling on the reliable one; a sales associate deciding how much discount to offer a repeat client; a team lead delegating a deadline to a colleague whose track record is mixed; a product manager deciding when an A/B test has run long enough.

Each has the same bones: options with unknown payoffs, feedback that arrives late and noisily, and a cost to both over-caution and over-confidence.

What the brain adds, and what it does not

Some of the clearest evidence about decision making comes from patients. In 1994 Bechara and colleagues reported that people with damage to the ventromedial prefrontal cortex, whose intelligence tests were otherwise normal, kept choosing card decks that paid well now and lost heavily later. They seemed, in the authors' words, guided by immediate prospects only. That task became the Iowa Gambling Task, the ancestor of our Card Decision game.

Brain findings like these tell you decision making is a real, separable capacity. They do not tell you how to decide better. For that you need the behavioural habits in the later lessons: think in averages over many rounds, update in proportion to the evidence, explore early and exploit late, and read other people by what they do rather than what you fear.

Remember

• Under risk you know the odds; under uncertainty you learn them. All four games teach the odds by experience.
• Expected value is the average payoff over many tries. It is the right yardstick for long runs of small choices.
• Losses weigh about twice as much as equal gains for most people, which pushes many into costly caution.
• Learning from feedback runs on prediction errors: update part of the way toward each new outcome.
• Explore early, while there is time to use what you learn; exploit once the evidence is in.
• With a counterpart, the odds depend on intentions. Read behaviour and adjust.

Next, what good decisions predict looks at the evidence linking these skills to real outcomes, and where that evidence is thin.

Sources

1. Hertwig, R., & Erev, I. (2009). The description–experience gap in risky choice. Trends in Cognitive Sciences, 13(12), 517–523. doi.org/10.1016/j.tics.2009.09.004
2. Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–291. doi.org/10.2307/1914185
3. Brown, A. L., Imai, T., Vieider, F. M., & Camerer, C. F. (2024). Meta-analysis of empirical estimates of loss aversion. Journal of Economic Literature, 62(2), 485–516. doi.org/10.1257/jel.20221698
4. Schultz, W., Dayan, P., & Montague, P. R. (1997). A neural substrate of prediction and reward. Science, 275(5306), 1593–1599. doi.org/10.1126/science.275.5306.1593
5. Daw, N. D., O'Doherty, J. P., Dayan, P., Seymour, B., & Dolan, R. J. (2006). Cortical substrates for exploratory decisions in humans. Nature, 441, 876–879. doi.org/10.1038/nature04766
6. Wilson, R. C., Geana, A., White, J. M., Ludvig, E. A., & Cohen, J. D. (2014). Humans use directed and random exploration to solve the explore–exploit dilemma. Journal of Experimental Psychology: General, 143(6), 2074–2081. doi.org/10.1037/a0038199
7. Alós-Ferrer, C., & Farolfi, F. (2019). Trust games and beyond. Frontiers in Neuroscience, 13, 887. doi.org/10.3389/fnins.2019.00887
8. Bechara, A., Damasio, A. R., Damasio, H., & Anderson, S. W. (1994). Insensitivity to future consequences following damage to human prefrontal cortex. Cognition, 50(1–3), 7–15. doi.org/10.1016/0010-0277(94)90018-3