Wisdom of the crowd

The wisdom of the crowd is the process of taking into account the collective opinion of a group of individuals rather than a single expert to answer a question. 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, and often better than, the answer given by any of the individuals within the group. An intuitive and often-cited explanation for this phenomenon is that there is idiosyncratic noise associated with each individual judgment, and taking the average over a large number of responses will go some way toward canceling the effect of this noise. This process, while not new to the information age, has been pushed into the mainstream spotlight by social information sites such as Wikipedia and Yahoo! Answers, and other web resources that rely on human opinion.

The process, in the business world at least, was written about in detail by James Surowiecki in his book The Wisdom of Crowds.

In the realm of justice, trial by jury can be understood as wisdom of the crowd, especially when compared to the alternative, trial by a judge, the single expert.

In the political domain, 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 within cognitive science has sought to model the relationship between wisdom of the crowd effects and individual cognition.

Classic examples

The classic wisdom-of-the-crowds finding involves point estimation of a continuous quantity. At a 1906 country fair in Plymouth, eight hundred people participated in a contest to estimate the weight of a slaughtered and dressed ox. Statistician Francis Galton observed that the mean of all eight hundred guesses, at 1197 pounds, was closer than any of the individual guesses to 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 mean centered near the true mean of the quantity to be estimated.

Definition of crowd

The term crowd, in this usage, refers to any group of people, such as a corporation, a group of researchers, or simply the entire general public. The group itself does not have to be cohesive; for example, a group of people answering questions on Yahoo! Answers may not know each other outside of that forum, or a group of people betting on a horse race may not know each others' bets, but they nevertheless form a crowd under this definition.

Benefits

The wisdom of the crowd applies to democratic journalism in that a group of non-experts determine what news is important, and then people outside the group can view the news based on those rankings. The social news sites Digg and Newsvine both fall into this category and rely heavily upon the wisdom of the crowd in creating their content.

Problems

Wisdom-of-the-crowds research routinely attributes the superiority of crowd averages over individual judgments to the elimination of individual noise, an explanation that assumes independence of the individual judgments from each other , . Thus the crowd tends to make its best decisions if it is made up of diverse opinions and ideologies.

Miller and Stevyers (in press) reduced the independence of individual responses in a wisdom-of-the-crowds experiment by allowing limited communication between participants. Participants were asked to answer ordering questions for general knowledge questions such as the order of U.S. presidents. For half of the questions, each participant started with the ordering submitted by another participant (and alerted to this fact), and for the other half, they started with a random ordering, and in both cases were asked to rearrange them (if necessary) to the correct order. Answers where participants started with another participant's ranking were on average more accurate than those from the random starting condition. Miller and Steyvers conclude that different item-level knowledge among participants is responsible for this phenomenon, and that participants integrated and augmented previous participants' knowledge with their own knowledge.

Crowds tend to work best when there is a correct answer to the question being posed, such as a question about geography or mathematics.

The wisdom of the crowd effect is easily undermined. Social influence can cause the average of the crowd answers to be wildly inaccurate, while the geometric mean and the median are far more robust.

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 (at least somewhat) statistically independent. Another caveat is that individual probability judgments are often biased toward extreme values (e.g., 0 or 1). 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 (2008) 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 (an anchoring effect) and were thus subject to (some of) 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.

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 salesperson problem, in which participants must the shortest route between an array of points. Models of these problems either break the problem into common pieces (the local decomposition method of aggregation) or find solutions that are most similar to the individual human solutions (the global similarity aggregation method),
• 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