Why KCL on that list ?!?
For Political Science, these are the top 10 departments according to the Shanghai ranking. In my view, the list looks fairly accurate.
1. LSE
2. University of Oxford
3. Aarhus University
4. University of Amsterdam
5. University College London
6. University of Zurich
7. University of Gothenburg
8. University of Essex
9. University of Oslo
10. ETH Zurich
But for a Ph.D in Political Science, choose an institution that provides you with adequate funding. If there is no funding, don't go!
This list isn't so bad, but U Zurich and Oslo should be replaced by Konstanz and Mannheim. ETH has good quality but is small. The order of the institutions on the list can't be reliably established. As pointed out above, being on the list merely means you have a higher probability of finding a good supervisor. Instead of top 10, maybe this would be a good revised top 14 list, without any specific order, hence listed alphabetically:
Amsterdam (University, not FU)
Aarhus
Essex
ETH Zurich
EUI
Gothenburg
KCL
Konstanz
Leiden
LSE
Mannheim
Oxford
UCL
Zurich (University)
Among the stronger institutions on that list are LSE, ETH (though small), Essex, and EUI. Among the relatively weaker ones are Zurich and Gothenburg.
Contenders for the next places below this list are institutions like Warwick, Bocconi, Geneva, Copenhagen, and Sciences Po.