The consequence of this is four-fold: First, global governance reform faces gridlock. Second, international institutions lose effectiveness and legitimacy. Third, formal European dominance in these institutions is rendered meaningless by the cacophony of European voices and lack of cohesion in votes. Fourth, Europe over time is increasingly marginalized in global decision making.
This outcome serves neither global nor European interests. It may be counter-intuitive, but if the Europeans give up votes and chairs in the international institutions, they will wield more influence in more effective global institutions.