This paper proposes an analytical framework to rank alternative measures of banks' systemic importance in terms of their welfare impact. The advantage of our approach is that it does not require knowing the exact mathematical form of the underlying welfare function in the absence of a widely accepted model of systemic risk. The framework consists of two pillars. First, economic welfare is linked to the measured degree of systemic importance of banks. Second, the association between the concepts of stochastic and welfare dominance of distributions of the measured degree of systemic importance is defined. Then, the alternative measures can be welfare‐ranked by just establishing stochastic dominance relationships. An illustration is presented using Luxembourg data. Copyright © 2015 John Wiley & Sons, Ltd.