Europe can contribute significantly to China's integration into global norms and institutions. In general, Europe and the US have more to fear from a weak China than they do from a wealthy China. Political Islam and how it develops will be the second factor. The struggle against extreme Islamist terrorism is not a "clash of civilizations," but a civil war within Islam. A radical minority is using violence to impose a simplified and ideological version on a mainstream with more diverse views.
Another major determinant of which scenario prevails will be US power and how it is used. The US will remain the most powerful country in 2020, but, paradoxically, the strongest state since the days of Rome will be unable to protect its citizens acting alone.
US military might is not adequate to deal with threats such as global pandemics, climate change, terrorism and international crime. These issues require cooperation in the provision of global public goods and the soft power of attracting support. No part of the world shares more values or has a greater capacity to influence US attitudes and power than does Europe. That suggests that the fourth political determinant of the future will be the evolution of European policies and power.
Joseph Nye is a professor at Harvard.
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