Combining an Odd (vs. an Even) Number of Forecasts with Fat-Tailed Forecast Error

Point estimates plus margins of error communicate statistical information to nonstatisticians. Although descriptive of bell-shaped probability distributions, they can be misleading for uniform or bi-modal distributions. Cooke shows that forecast errors are often described by fat-tailed distributions. Although the fat-tailed Cauchy distribution is bell shaped, the Bayesian combination of multiple Cauchy forecasts can be bell shaped, multimodal, or have a flat maximum. When forecast variation is intermediate, the combined forecast will only be bell shaped when the number of forecasts is odd. In this case, point estimates with margins of error can be informative.