Abstract

People usually tell the story of Sir Francis Galton's visit to the West of England Fat Stock and Poultry Exhibition in 1906  as follows: Upon his visit, Galton came across a competition where the objective for participants was to guess the weight of an ox, after it had been slaughtered and prepared according to standard practice. Being convinced that elites should govern societies, it dawned upon Galton that if he could obtain access to the guesses submitted by participants, he could demonstrate just how far the median guess was from the objective truth, and thereby provide convincing support for his political perspective. As the usual story goes, however, Galton was surprised by what he discovered when he analyzed the data provided to him: the meat weighed 1198 lb. and the median overestimated by only 10 lb., but even more remarkably, the mean underestimated by merely 1.23 lb. Galton's trust in democratic judgment changed, the marvel that is the wisdom of crowds could be sold (Surowiecki) as popular science, and economists (Muth) could build the rational expectations hypothesis upon it.

Another story completes the account that Galton openly told in Nature the year after his visit. While Galton was undoubtedly interested in the average guess, his interest hardly stopped there. Instead, the shape of the entire distribution struck Galton as curious. The distribution was negatively skewed and appeared to consist of two separate pieces, something which puzzled Galton so much that he ultimately had to admit defeat; he did not have sufficient knowledge of psychology to provide an adequate answer to why the distribution looked like it did. Galton did, however, suspect the work of Fechner and other psychophysicists held the key to his observation. Few people have paid much attention to that part.

In my talk at the Interacting Minds Centre on 28th May, I will provide an account of my work to address Galton's puzzle, and in particular, the development of the AQ model of magnitude estimation, which goes some way to explain why Galton observed what he did. I will also provide some perspective on the possible applications of the AQ in modeling situations where the dial of rationality and adherence to known psychophysical effects are essential.

Link to article in Journal of Mathematical Psychology 

About the speaker

Ulrik William Nash, SDU    

Department of Marketing & Management