Looks like third party arbitration. Guessing it ends up being reputation enforced.

   As there is no concept of arbitrator reputation, it makes
   no sense to deselect arbitrators, as this will only 
   reduce his trading possibilities. Traders will only be 
   able to take offers of users with whom they have at least
   one overlapping selected arbitrator

- http://bitsquare.io/arbitration_system.pdf

It looks like this is only required for withdrawing to a national currency (USD, EUR, etc). Being able to trade between altcoins trustlessly is pretty neat.