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How many gummy bears are in this picture?
If you’re anything like me, you will struggle with the question. Given the many blurred and half-covered shapes, counting is an unreliable strategy. Based on your previous experience of munching gummy bears, you may have some intuition about the quantity. I, for one, am pretty sure that there aren’t nearly enough gummy bears to satisfy my husband’s sweet tooth. Suggesting an exact number, however, is surprisingly tough.
Diversity of judgement
In situations of uncertainty, we often turn to our friends and family for advice. I thought I’d use the same strategy for solving my gummy bear problem, and asked 25 recent phone contacts for their guesses. Out of 25 people contacted, 23 replied (presumably, the rest were too busy). The lowest guess was 2 and the highest 297. The surprising spread of the responses is illustrated by the graph below, where the horizontal axis displays the number of gummy bears guessed and the vertical axis the frequency of each guess. With four votes, the most frequent guess was 50.
As demonstrated in this little exercise, people vary greatly in their personal judgements. Ask a hundred different people for their guesses and you get a hundred different responses—maybe more. At first glance, this diversity may seem frustrating. How can we identify the correct number of gummy bears if there is this much disagreement across our advisers? Whose opinion should we trust?
The wisdom of crowds
The answer is surprisingly simple: We should trust the crowd. In line with the popular proverb “two heads are better than one," research shows that rather than relying on any single opinion, the best approach is often to consider all advisers’ diverse judgements and then follow the crowd’s average response. Amazingly, in some cases the average group judgement may be even better than the response of the group’s smartest member.
The surprising accuracy of a group's combined judgements is referred to as “wisdom of crowds” or “collective intelligence." The phenomenon is typically attributed to a crowd’s diversity, which helps to cancel out extreme individual judgements. This means that instead of bemoaning differences in opinion, we should be grateful for our large spread of opinions regarding the number of gummy bears. Crucially, for crowd intelligence to work, each crowd member’s opinion has to be independent. This means that the judgement has to be made without prior conferral with other people, who could influence or bias the opinion. Relying on the wisdom of crowds is therefore different from team-based decision making, in which group members discuss their judgements before reaching a jointly agreed group decision.
Evidence for the wisdom of crowds has been provided by a large number of experimental studies from the field of judgement and decision-making psychology. The experiments show that crowd-based judgements are more accurate than individual judgements across many different decision contexts including knowledge tests, memory tasks, and combinatorial problems. Additionally, a growing number of studies have demonstrated the potential of the wisdom of crowds in more applied contexts of medical decision making. A recent computer-simulation study, for example, suggested that medical students’ diagnoses for patients in emergency care could be improved through an aggregation of two or more opinions.
Harnessing crowd wisdom
To harness the wisdom of crowds for solving specific decision-making problems, anonymous judgments of crowd members need to be collected and combined according to a predefined crowd rule. Most crowd rules aim to average the judgements of all decision makers, but the specific rules may need to be adjusted based on the observed pattern of responses.
For example, in the context of our gummy bear guessing game, there may be different ways of generating a crowd average. Calculating the crowd mean (adding up all responses and dividing the sum by the number of people in the crowd) is one option. In the case of my own little experiment drawing on a group of 23 friends, the crowd mean was 65.
Calculating the mean may be a good approach in many cases, but it can be misleading if the responses contain extreme outliers (i.e., a few guesses that are very different from the rest). Looking at our graph of responses, 22 out of 23 people (i.e., 96% of the entire crowd) suggested numbers equal to or lower than 200. The one person who suggested a number of 297 might therefore be considered an outlier. Given that every response makes an equal contribution to the calculation of the mean, this extreme response at the top end of the range is likely to have had a disproportionately large influence on our average result. Alternative crowd rules could avoid this potential downfall. By calculating the median value (i.e., the middle point of all judgements) or the modal value (i.e., the most frequent judgement), for example, a more "conservative" group guess of 50 can be derived.
Finally, for some types of problems, it might be necessary to select specific crowds with relevant expertise. While anybody can offer a guess about the number of sweets displayed in a photograph, other choice contexts may require prior experience. Imagine, for example, that you are trying to find the best yoga mat on the market. Rather than asking a random group of people for their judgments, it may be more helpful to selectively ask regular yoga practitioners.
How many gummy bears are in the picture?
Due to its extreme diversity, a crowd's combined knowledge often surpasses that of individual decision makers. An anonymous aggregation of independent judgments can therefore be a promising way of achieving more accurate problem solutions. Indeed, gathering the "wisdom of crowds" might yield better results compared to team-based decision processes, which frequently introduce bias through the influences of overconfident and persuasive team members. However, while the literature presented in this post provides overall support for the wisdom of crowds, it is necessary to consider the problem context before harnessing the power of diversity. Based on the nature of the problem or the pattern of responses, different crowd rules may be required to optimise the outcome.
Returning to our initial dilemma of determining the number of gummy bears in the photograph, the collective intelligence gathered from my pool of friends suggests answers of 65 or 50, depending on the crowd rule. If you were hoping to learn the correct answer, I am sorry to disappoint you. I have no idea exactly how many gummy bears are displayed in the picture. However, why don’t you run your own little survey and assess the wisdom of crowds? The bigger the group of participants and the more diverse its members, the closer the group guess is going to be to the true answer. Please share your results in the comments!
