Measuring the Wisdom of the Crowd: How Many is Enough?

The idea of the wisdom of the crowd is that integrating multiple estimates of a group of individuals provides an outcome that is often better than most of the underlying estimates or even better than the best individual estimate. In this paper, we examine the wisdom of the crowd principle on the example of spatial data collection by paid crowdworkers. We developed a web-based user interface for the collection of vehicles from rasterized shadings derived from 3D point clouds and executed different data collection campaigns on the crowdsourcing marketplace microWorkers. Our main question is: how large must be the crowd in order that the quality of the outcome fulfils the quality requirements of a specific application? To answer this question, we computed precision, recall, F1 score, and geometric quality measures for different crowd sizes. We found that increasing the crowd size improves the quality of the outcome. This improvement is quite large at the beginning and gradually decreases with larger crowd sizes. These findings confirm the wisdom of the crowd principle and help to find an optimum number of the crowd size that is in the end a compromise between data quality, and cost and time required to perform the data collection.