On Peirce’s Motivation for Equitability in Forecast Verification

In 1884, Peirce proposed a new two-category score for deterministic forecasts. The score was motivated by the desire to estimate the number of correct forecasts based on sound reasoning, without being sensitive to the frequency distribution of any residual random component of the forecast system. At the end of his article, Peirce pondered the situation of more than two categories and stated “I have a solution for this case.” Alas, it does not appear that he published this. Here, a simple calculation demonstrates a possible solution. Interestingly, it leads directly to the equitability constraints proposed over a hundred years later by Gandin and Murphy. Indeed, Peirce’s motivation provides a compelling and complementary justification for the use of equitability in scoring.