Public Choice, My Dear Watson

Sherlock Holmes is such a popular fictional character because of how differently he behaves from the average person. Sherlock Holmes cares little about the impressions others have of him (except when theatrically proving the police wrong with a solution to a case), and instead pursues private utility at all costs. Although some psychologists have described Sherlock Holmes as psychopathic (to which, in the modern-day television adaptation, Holmes responds that he is merely a high-functioning sociopath), perhaps he can be better described as an approximation of a perfectly rational, utility-maximizing individual for the purposes of economic modeling.

In the first Sherlock Holmes novel, A Study in Scarlet, Dr. Watson reflects upon Sherlock Holmes’s startling ignorance in many common fields of knowledge. Although Holmes knows the details of every murder committed in London in recent memory and can deduce the brand of cigar used by a suspect by glancing at an ashtray, he shows a perplexing dearth of knowledge in many other areas. The reader learns that Sherlock Holmes does not know that the earth travels around the sun, and also knows no information about philosophy or literature. Although this lack of knowledge is surprising for someone as brilliant as Sherlock Holmes, Sherlock actually seeks a rational level of ignorance. The following is a graph of Sherlock Holmes’s allocatively efficient level of ignorance for astronomy compared to that of the average population. 

To start, Holmes’s private marginal benefit of learning astronomy is lower than that of the average person. He cares very little about ever needing basic astronomy information for day-to-day conversation due to his diminished desire for social approval, and he is also certain he will not need to understand astronomy for his detective work. His private marginal cost of learning astronomy is higher than that of the average person as well, because the opportunity cost of maintaining his occupational reputation as genius private detective is advanced time spent researching specific subjects and developing his deductive reasoning ability. As a result, the allocatively efficient level of knowledge of astronomy for Sherlock Holmes is extremely low.

One of Sherlock Holmes's under-appreciated attributes is that he represents a utility-maximizing actor in an economic system. A world where everyone is a little more like Sherlock Holmes might be a less friendly place, but at least it would improve the applicability of economic models.