Wisdom of The Crowd - Higher-dimensional Problems and Modeling

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 find 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