Wisdom of the crowd
"Wisdom of the crowd" or "wisdom of the majority" expresses the notion that the collective opinion of a diverse and independent group of individuals yields the best judgement. This concept, while not new to the Information Age, has been pushed into the spotlight by social information sites such as Quora, Reddit, Stack Exchange, Wikipedia, Yahoo! Answers, and other web resources which rely on collective human knowledge. An explanation for this supposition is that the idiosyncratic noise associated with each individual judgment is replaced by an average of that noise taken over a large number of responses, tempering the effect of the noise.
Trial by jury can be understood as at least partly relying on wisdom of the crowd, compared to bench trial which relies on one or a few experts. In politics, sometimes sortition is held as an example of what wisdom of the crowd would look like. Decision-making would happen by a diverse group instead of by a fairly homogenous political group or party. Research in cognitive science has sought to model the relationship between wisdom of the crowd effects and individual cognition.
A large group's aggregated answers to questions involving quantity estimation, general world knowledge, and spatial reasoning has generally been found to be as good as, but often superior to, the answer given by any of the individuals within the group.
Jury theorems from social choice theory provide formal arguments for wisdom of the crowd given a variety of more or less plausible assumptions. Both the assumptions and the conclusions remain controversial, even though the theorems themselves are not. The oldest and simplest is Condorcet's jury theorem.
Examples
is credited as the first person to write about the "wisdom of the crowd" in his work Politics. According to Aristotle, "it is possible that the many, though not individually good men, yet when they come together may be better, not individually but collectively, than those who are so, just as public dinners to which many contribute are better than those supplied at one man's cost".File:Sir Francis Galton by Charles Wellington Furse.jpg|thumb|Sir Francis Galton by Charles Wellington Furse, given to the National Portrait Gallery, London in 1954
The classic wisdom-of-the-crowds finding involves point estimation of a continuous quantity. At a 1906 country fair in Plymouth, 800 people participated in a contest to estimate the weight of a slaughtered and dressed ox. Statistician Francis Galton observed that the median guess, 1207 pounds, was accurate within 1% of the true weight of 1198 pounds. This has contributed to the insight in cognitive science that a crowd's individual judgments can be modeled as a probability distribution of responses with the median centered near the true value of the quantity to be estimated.
In recent years, the "wisdom of the crowd" phenomenon has been leveraged in business strategy, advertising spaces, and also political research. Marketing firms aggregate consumer feedback and brand impressions for clients. Meanwhile, companies such as Trada invoke crowds to design advertisements based on clients' requirements. Lastly, political preferences are aggregated to predict or nowcast political elections.
Higher-dimensional problems and modeling
Although classic wisdom-of-the-crowds findings center on point estimates of single continuous quantities, the phenomenon also scales up to higher-dimensional problems that do not lend themselves to aggregation methods such as taking the mean. More complex models have been developed for these purposes. A few examples of higher-dimensional problems that exhibit wisdom-of-the-crowds effects include:- Combinatorial problems such as minimum spanning trees and the traveling salesman problem, in which participants must find the shortest route between an array of points. Models of these problems either break the problem into common pieces or find solutions that are most similar to the individual human solutions.
- Ordering problems such as the order of the U.S. presidents or world cities by population. A useful approach in this situation is Thurstonian modeling, which each participant has access to the ground truth ordering but with varying degrees of stochastic noise, leading to variance in the final ordering given by different individuals.
- Multi-armed bandit problems, in which participants choose from a set of alternatives with fixed but unknown reward rates with the goal of maximizing return after a number of trials. To accommodate mixtures of decision processes and individual differences in probabilities of winning and staying with a given alternative versus losing and shifting to another alternative, hierarchical Bayesian models have been employed which include parameters for individual people drawn from Gaussian distributions.
Surprisingly popular
Definition of crowd
In the context of wisdom of the crowd, the term crowd takes on a broad meaning. One definition characterizes a crowd as a group of people amassed by an open call for participation.In the digital age, the potential for collective intelligence has expanded with the advent of information technologies and social media platforms such as Google, Facebook, Twitter, and others. These platforms enable the aggregation of opinions and knowledge on a massive scale, creating what some have defined as "intelligent communities." However, the effectiveness of these digital crowds can be compromised by issues such as demographic biases, the influence of highly active users, and the presence of bots, which can skew the diversity and independence necessary for a crowd to be truly wise. To mitigate these issues, researchers have suggested using a multi-media approach to aggregate intelligence from various platforms or employing factor analysis to filter out biases and noise.
While crowds are often leveraged in online applications, they can also be utilized in offline contexts. In some cases, members of a crowd may be offered monetary incentives for participation. Certain applications of "wisdom of the crowd", such as jury duty in the United States, mandate crowd participation.
Analogues with individual cognition: the "crowd within"
The insight that crowd responses to an estimation task can be modeled as a sample from a probability distribution invites comparisons with individual cognition. In particular, it is possible that individual cognition is probabilistic in the sense that individual estimates are drawn from an "internal probability distribution." If this is the case, then two or more estimates of the same quantity from the same person should average to a value closer to ground truth than either of the individual judgments, since the effect of statistical noise within each of these judgments is reduced. This of course rests on the assumption that the noise associated with each judgment is statistically independent. Thus, the crowd needs to be independent but also diversified, in order to allow a variety of answers. The answers on the ends of the spectrum will cancel each other, allowing the wisdom of the crowd phenomena to take its place. Another caveat is that individual probability judgments are often biased toward extreme values. Thus any beneficial effect of multiple judgments from the same person is likely to be limited to samples from an unbiased distribution.Vul and Pashler asked participants for point estimates of continuous quantities associated with general world knowledge, such as "What percentage of the world's airports are in the United States?" Without being alerted to the procedure in advance, half of the participants were immediately asked to make a second, different guess in response to the same question, and the other half were asked to do this three weeks later. The average of a participant's two guesses was more accurate than either individual guess. Furthermore, the averages of guesses made in the three-week delay condition were more accurate than guesses made in immediate succession. One explanation of this effect is that guesses in the immediate condition were less independent of each other and were thus subject to the same kind of noise. In general, these results suggest that individual cognition may indeed be subject to an internal probability distribution characterized by stochastic noise, rather than consistently producing the best answer based on all the knowledge a person has. These results were mostly confirmed in a high-powered pre-registered replication. The only result that was not fully replicated was that a delay in the second guess generates a better estimate.
Hourihan and Benjamin tested the hypothesis that the estimate improvements observed by Vul and Pashler in the delayed responding condition were the result of increased independence of the estimates. To do this Hourihan and Benjamin capitalized on variations in memory span among their participants. In support they found that averaging repeated estimates of those with lower memory spans showed greater estimate improvements than the averaging the repeated estimates of those with larger memory spans.
Rauhut and Lorenz expanded on this research by again asking participants to make estimates of continuous quantities related to real world knowledge. In this case participants were informed that they would make five consecutive estimates. This approach allowed the researchers to determine, firstly, the number of times one needs to ask oneself in order to match the accuracy of asking others and then, the rate at which estimates made by oneself improve estimates compared to asking others. The authors concluded that asking oneself an infinite number of times does not surpass the accuracy of asking just one other individual. Overall, they found little support for a so-called "mental distribution" from which individuals draw their estimates; in fact, they found that in some cases asking oneself multiple times actually reduces accuracy. Ultimately, they argue that the results of Vul and Pashler overestimate the wisdom of the "crowd within" – as their results show that asking oneself more than three times actually reduces accuracy to levels below that reported by Vul and Pashler.
Müller-Trede attempted to investigate the types of questions in which utilizing the "crowd within" is most effective. He found that while accuracy gains were smaller than would be expected from averaging ones' estimates with another individual, repeated judgments lead to increases in accuracy for both year estimation questions and questions about estimated percentages. General numerical questions did not improve with repeated judgments, while averaging individual judgments with those of a random other did improve accuracy. This, Müller-Trede argues, is the result of the bounds implied by year and percentage questions.
Van Dolder and Van den Assem studied the "crowd within" using a large database from three estimation competitions organised by Holland Casino. For each of these competitions, they find that within-person aggregation indeed improves accuracy of estimates. Furthermore, they also confirm that this method works better if there is a time delay between subsequent judgments. Even with considerable delay between estimates, between-person aggregation is more beneficial. The average of a large number of judgements from the same person is barely better than the average of two judgements from different people.