For politics how will you measure political astuteness, procedural knowledge, and the ability to gauge the public and the leaderships attitudes and moods? How about the ability to wrangle a deal that matters to the person more than to their represented interests, or more one set of interests over another?
These are all social skills in my eyes. They all come under Ganymede's Guile, representing knowledge of options, and the ability to assess which approaches will be most likely get you want you want the most effectively.
To me politics are all about external interests, effectively a ton of markers, some of which are mutual exclusive, some of partially exclusive (such as which port gets the trade deal), and many are just little things that are the base currency of doing your job representing the people/assets you do.
It can't all be cold hard math. There has to be more need than resources, which forces choices, which can enable tradeoffs, which can cause people and places to rise or decline. So its people, and that means social skills.