The political blessings of federalism are the core of our discussion. These benefits are operationalized as the decrease in the number of outvoted in a federal system with majority voting as an important source of regime satisfaction. The approach originates from the work of Roland Pennock who developed a similar methodology exactly 50 years ago although he applied it to a slightly different topic. First, we show that decentralized decision-making is advantageous in the majority of logical cases since the expected value of the number of outvoted is lower compared to centralized decision-making. Comparing different cases, we conclude that the political force of the decentralization-theorem (Oates) is a sole and inverse function of the population size of the nation, implying that there is no structural effect of differing populations within regions. Next, the question is addressed how the gains from federalism react to variations in the number of regions: Measured as the difference of the shares of the sum of the highest number of outvoted to the national population between federalism and centralism, the gains of federalism are a direct function of the number of regions, in a 3-regions-case as well as in a generalized formal model. Therefore, a decrease of the population at the national level and an increase of the number of regions boost the gains of federalism representing a successful path to enhance regime satisfaction. The complementary question what happens to the gains of federalism when increasing the number of alternatives to vote for is more difficult to answer for set-ups with more than 2 alternatives. In our special case with 2 regions and 3 alternatives, the model shows that augmenting the number of alternatives exerts a negative effect on the gains of federalism if we use our first indicator - the share of the sum of the highest number of outvoted. If instead we employ the shares of the average number of outvoted, then there is still a slight increase in the gains of federalism. Using the last indicator, a case-related comparison of both effects shows that an increase in the number of regions has a stronger positive impact on the gains than letting the number of alternatives grow. Employing the other indicator of the share of the sum of the highest number of outvoted, then there is clearly a positive effect of the number of regions. But the effect of the number of alternatives is negative, implying that this last indicator underestimates the gains of federalism to a certain extent. Our integrative model explaining the gains of federalism reconfirms these interdependencies with the share of the sum of the highest numbers of outvoted: The first derivative is positive for more than 2 regions and the same holds for the size of the population at the national level in an unrestricted manner. Differentiating the number of alternatives, however, leads to a casuistic of 4 different domains separating positive and negative effects. Finally, we return to the opening question by analyzing the cumulative frequency distributions of the number of outvoted: Here, even if federalization is preferable as a whole, centralized decision-making is more advantageous for low numbers of outvoted, implying that the domain of decentralized decision-making seems to be connected to higher levels of the outvoted.