Numerous studies have used monadic or dyadic data to show that democracies are more likely to win wars. Poast (2010; Political Analysis 18(4): 403–425) demonstrates that the use of dyadic data to model events that are really multilateral (or k-adic) can bias the statistical results. In this article, I discuss the potential consequences of that bias for previous studies on democracy and war outcomes. Then I replicate some of those studies using modified, k-adic versions of the original datasets. Finally, I conduct an original analysis using the updated dataset on wars by Reiter et al. (2014a; Journal of Conflict Resolution; doi: 10.1177/0022002714553107). Overall, I find several changes when using k-adic data. Most significantly, the relationship between democracy and war outcomes appears to be strongest for states that join the war effort after it has already started.