What determines the allocation of voting weights to member states in international organizations? What drives the seat and voting weight allocation in the European Parliament (EP) and in the Council of the European Union (EU)? Our objective in this article is to develop a universal logical model and to demonstrate that the resulting equation indeed captures negotiated outcomes on seat and voting weight allocations in EU institutions from their beginning. We predict seat and voting weight allocations for both the EP and the Council of the EU within one general model. Hence, we do not employ actual data on seat allocations or voting weights in either the EP or the Council of the EU, but instead, use logical constraints exclusively, as posed by the following elements: the total number of seats/voting weights (S), the number of member states (N) and, finally, their respective population size (P i). Only our final model selection among several theoretical options is guided by empirical information. With no post hoc parameters used, our model fits both the Council of the EU and the EP rather well, over a time span of nearly 40 years. Inspired by the 'seat-vote equation' (Taagepera, 1973) for seat allocation in national legislatures, the new 'seat-population equation' calculates the number (S i) of EP seats or Council voting weights of member state i as follows: S i = SP in/∑P in, where n = (1/logN - 1/log S)/(1/logN - 1/log P), P being the total population (as summed over all member states). We posit that this equation is applicable to predict outcomes in practice whenever voting weight or seat allocations in international organizations are allocated on the basis of the population shares of their component entities. © 2006 political studies association.