This article presents a framework for evaluation of the impact of languages in multilingual societies. We consider several ranking methods based on various principles, including minimal disenfranchisement, communicative benefits, utilitarianism, and the game-theoretical concept of the Shapley Value. We use data from a Special Barometer survey to apply these methods to languages within the European Union and conclude that they generate quite consistent results. Finally, we analyse the impact of Brexit on the rankings, especially in the case where English forfeits its status as an official language of the Union. 1 The first author is grateful to Michel Vanden Abeele for clarifications on the status of English if Brexit takes place and to Israel Zang for unending discussions on Shapley ranking. The second author acknowledges financial support from the Spanish Ministry of Economics and Competitiveness through the research project ECO2014-57413-P. The third author wishes to thank the Russian Science Foundation for its financial support through the research project #15 − 18 − 00098. The detailed comments by seminar participants at UMASS, Amherst, two anonymous referees, as well as an associate editor of this journal are gratefully acknowledged.