In Protocol 7, a voter's vote is very secure. Any conspiracy of other voters gains no additional information beyond that already known by the corrupt voters unless they are able to break the encryption scheme. Only a conspiracy of pDT corrupt authorities, can compromise a voter's vote. Once this many authorities are corrupt, however, all votes are compromised.
In our protocol, a voter enjoys the same protection from other voters, but the situation with authorities becomes less clear. As in the case with Protocol 7, a voter's vote can be compromised only by corrupting enough authorities. Here, however, there are fewer authorities to corrupt; to discover a voter's vote, an adversary need only collect information from a sufficient number of authorities in a voter's district, namely pT.
More generally, our protocol is more vulnerable to an adversary which can dynamically corrupt a certain number of authorities; such an adversary can determine any individual vote it wishes. At a broader level, however, to discover every voter's vote still requires an adversary to corrupt pT authorities in each district, or pDToverall.
Naturally, if a protocol using sum secret sharing (such as Protocol 6 or subset authority voting) is used, a similar situation results. In Protocol 6 all of the authorities need to be corrupted; in subset authority voting all of the authorities in a district need to be corrupted.