Losing a coin toss makes it feel less fair

Let's say you and a friend have plans to go out to dinner. You want to try a local Indian restaurant, while your friend prefers the idea of Italian. What fairer way could there be to settle this than with a random coin toss?

If your friend flipped the coin and won, though, would you feel that the result was somehow less fair than if they'd flipped the coin and lost? If so, you'd be in the same boat as thousands of participants in a new study in the Journal of Personality and Social Psychology: Attitudes and Social Cognition that demonstrates an 'illusion of unfairness' in coin flips. This work, led by Rémy A. Furrer at the University of Virginia, reveals an example of human irrationality, and potentially one with some serious implications.

The team ran a total of 11 studies on almost 6,000 people. In every one, the participants believed that a coin flip would decide who in a pair would receive a good outcome, and who would receive a bad one.

In two initial lab studies, the researchers told student participants that they, plus one other person, would be taking part in a learning task. They were also told that a coin flip would decide who would receive a snack for every correct answer, and who would have to plunge their hand into a bucket of ice water for each incorrect answer.

In the first study, a confederate played the role of the second participant, and a coin with either two heads or two tails ensured that the actual participant lost the toss. In the second study, two actual participants took part, and one was given the coin to toss. Afterwards, they were all asked questions that probed how they felt about the process.

The team also ran another seven variations on this coin-flip experiment, some on pairs of passersby in a park, other using online participants. In the online studies, virtual coin flips replaced the real thing, and small financial rewards were used instead of snacks, while the punishment was doing a boring task.

The team then meta-analysed the results of these nine studies, and found that people who lost the flip when they didn't flip the coin themselves thought that the coin-tossing procedure and the outcome were less fair. They also felt that they were less deserving of and less responsible for the outcome — and that they were less pleased, less happy, and liked the other participant less than when they had flipped the coin themselves.

The outcomes of coin tosses are random. (Or, at least very close to random.) So, the authors write, these findings demonstrate that their participants experienced an "illusion of unfairness".

The team also separately analysed the results from all the participants who had won coin tosses. They found that those who won after flipping the coin themselves reported that the procedure and outcome were less fair than when someone else had flipped. They also felt more responsible for the outcome, and more guilty about it. These results suggest that the illusion of unfairness is underpinned by the mistaken idea that we have some kind of control over the result of a coin flip.

In further studies, the researchers found that even before participants learned the result of a flip, they felt it was less fair that the other person got to flip the coin. Explaining that the decision about who should flip was random didn't make it seem any fairer. However, a final study did suggest that there is a way to combat the illusion.

All of the participants in this study didn't flip the coin themselves, and lost. They were asked to give either their "immediate gut reaction" or their "logical reasoned response" to the coin-flip process.

Those in the gut reaction group rated the procedure and outcome as the least fair. They were also less happy and more angry than the participants who'd made a reasoned response. This suggests, the team writes, that the illusion of fairness is a quick default response that can be corrected at least to some extent with further deliberation.

This new work does have a number of limitations. For example, all the participants were American (other cultures might respond differently), and the participants didn't know their partner (knowing the other person might affect how we feel, for better or for worse).

However, its findings might help to explain our behaviour in some other situations, too. For example, stating our feelings at work, or in a courthouse — even if we know, objectively, it won't influence a decision — might give us the illusion of having some kind of control over the outcome, and make any conclusions seem fairer. The team feels that their findings raise the possibility "that perceptions of control (albeit illusory ones) influence judgements of fairness in a fundamental way."

Read the paper in full:
Furrer, R. A., Wilson, T. D., & Gilbert, D. T. (2025). An illusion of unfairness in random coin flips. Journal of Personality and Social Psychology. Advance online publication. https://doi.org/10.1037/pspa0000447

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