You are asking about cable sizes without giving us particulars of the length of each leg and the intended loading, which are two of the prime factors. The position of the sockets around the length of the ring will affect the voltage drop and you cannot simply apply a standard formula unless the load is evenly distributed along the length.
If all the sockets are clustered together with two long, nearly equal legs back to the board, then the voltage drop will be similar to a radial made of a cable of twice the CSA. E.g. if your ring is made of 6mm² running 100m to the first point, then 5m between each point and the next, then 100m back to the board, you effectively have a 12mm² radial with the same voltage drop and CCC. I would instead use a radial of 16mm², terminated in an adaptable box to bring it down to 4mm² and run that along the sockets as a radial.
If instead the sockets are distributed along the length of the cable, then the ring or two radials would be a better bet. With an evenly distributed load, the drop in a ring is the same if you consider the middle point broken, making it two radials of half the total length. Then, each radial has a load equivalent to half the total, at a point halfway along. In this case it doesn't matter whether the circuit is a ring or radials, the drop is equal. Since the voltage drop is probably going to dictate the cable size instead of the CCC, you might be better off with double the number of radials.