Looks pretty good. Ill help test.
Several things though:
1. It does seem a bit unbalanced, and many of the bonuses seem awfully large. obviously, owning Peter I Island is a huge advantage.
2. I would try to use the actual names for the regions, especially the islands. Here's a map: http://www.geoatlas.com/medias/maps/continents/antarctica/a0tyi01a/antarctica_pol.jpg
. If you would like, I can go through and come up with names for each of the territories for you. Just let me know.
3. There is a Chilean claim between Marie Byrd Land and the UK claim. Its not included on your map... intentional?
4. Simplify some of your paths: (New Zealand lands 1, 2, and 3; Unclaimed outer, inner, south pole, and island 1; Australia Inner, outer and 5; Norway land outer 2; and UK Peninsula and islands 1 and 2.)
5: Use the "Snap-to cusp nodes" function of Inkscape, especially for the centre. This will help align all the central territories so they essentially come to the same point, and the map will look more uniform.
6: Its not obvious that UK land 3 and Unclaimed island 1 are connected. Perhaps a connection line would clear that up.
7: You're missing connections between UK land 1 and Norway land Outer 1 and inner 1.