Underpowered Power Law Research and the Decline-of-War Question

We challenge two key aspects of the decline-of-war critiques advanced by Clauset (2018) and Braumoeller (2019): what we call the "unchanging power-law argument" and the "unchanging arrival-rate argument." The former argument claims no decline in the risk of large wars post-1945 because war sizes fit a single power-law distribution before and after 1945. We counter by showing that evidence for power-law distributions in war sizes is weak, demonstrating that alternative fat-tailed distributions may better model war sizes, highlighting the limitations of extrapolating such laws beyond observed data ranges and showing that tests to detect changes in power-law parameters are underpowered. The latter argument, the "unchanging arrival-rate argument," claims constant war occurrence rates across periods but we argue that tests to detect changes in war-arrival rates are also underpowered. A substantial post-1945 decline might go undetected because the tests lack the sensitivity to identify even substantively very large changes in arrival rates. We conclude that more comprehensive data sets and methodologies are required for robust conclusions regarding the decline-of-war thesis.