We examined the trade-off between the cost of response redundancy and the gain in output quality on the popular crowdsourcing platform Mechanical Turk, as a partial replication of Kosinski et al. (2012) who demonstrated a significant improvement in performance by aggregating multiple responses through majority vote. We submitted single items from a validated intelligence test as Human Intelligence Tasks (HITs) and aggregated the responses from “virtual groups” consisting of 1 to 24 workers. While the original study relied on resampling from a relatively small number of responses across a range of experimental conditions, we randomly and independently sampled from a large number of HITs, focusing only on the main effect of group size. We found that – on average – a group of six MTurkers has a collective IQ one standard deviation above the mean for the general population, thus demonstrating a “wisdom of the crowd” effect. The relationship between group size and collective IQ was characterised by diminishing returns, suggesting moderately sized groups provide the best return on investment. We also analysed performance of a smaller subset of workers who had each completed all 60 test items, allowing for a direct comparison between a group’s collective IQ and the individual IQ of its members. This demonstrated that randomly selected groups collectively equalled the performance of the best-performing individual within the group. Our findings support the idea that substantial intellectual capacity can be gained through crowdsourcing, contingent on moderate redundancy built into the task request.

We consider the recently-developed “surprisingly popular” method for aggregating decisions across a group of people (Prelec, Seung and McCoy, 2017). The method has shown impressive performance in a range of decision-making situations, but typically for situations in which the correct answer is already established. We consider the ability of the surprisingly popular method to make predictions in a situation where the correct answer does not exist at the time people are asked to make decisions. Specifically, we tested its ability to predict the winners of the 256 US National Football League (NFL) games in the 2017–2018 season. Each of these predictions used participants who self-rated as “extremely knowledgeable” about the NFL, drawn from a set of 100 participants recruited through Amazon Mechanical Turk (AMT). We compare the accuracy and calibration of the surprisingly popular method to a variety of alternatives: the mode and confidence-weighted predictions of the expert AMT participants, the individual and aggregated predictions of media experts, and a statistical Elo method based on the performance histories of the NFL teams. Our results are exploratory, and need replication, but we find that the surprisingly popular method outperforms all of these alternatives, and has reasonable calibration properties relating the confidence of its predictions to the accuracy of those predictions.

We demonstrate the usefulness of cognitive models for combining human estimates of probabilities in two experiments. The first experiment involves people’s estimates of probabilities for general knowledge questions such as “What percentage of the world’s population speaks English as a first language?” The second experiment involves people’s estimates of probabilities in football (soccer) games, such as “What is the probability a team leading 1–0 at half time will win the game?”, with ground truths based on analysis of large corpus of games played in the past decade. In both experiments, we collect people’s probability estimates, and develop a cognitive model of the estimation process, including assumptions about the calibration of probabilities and individual differences. We show that the cognitive model approach outperforms standard statistical aggregation methods like the mean and the median for both experiments and, unlike most previous related work, is able to make good predictions in a fully unsupervised setting. We also show that the parameters inferred as part of the cognitive modeling, involving calibration and expertise, provide useful measures of the cognitive characteristics of individuals. We argue that the cognitive approach has the advantage of aggregating over latent human knowledge rather than observed estimates, and emphasize that it can be applied in predictive settings where answers are not yet available.

We consider the wisdom of the crowd situation in which individuals make binary decisions, and the majority answer is used as the group decision. Using data sets from nine different domains, we examine the relationship between the size of the majority and the accuracy of the crowd decisions. We find empirically that these calibration curves take many different forms for different domains, and the distribution of majority sizes over decisions in a domain also varies widely. We develop a growth model for inferring and interpreting the calibration curve in a domain, and apply it to the same nine data sets using Bayesian methods. The modeling approach is able to infer important qualitative properties of a domain, such as whether it involves decisions that have ground truths or are inherently uncertain. It is also able to make inferences about important quantitative properties of a domain, such as how quickly the crowd accuracy increases as the size of the majority increases. We discuss potential applications of the measurement model, and the need to develop a psychological account of the variety of calibration curves that evidently exist.