Suppose an anonymous organisation has the ability to take control of the minds of any people they chose, as long as they are able to identify who it is they want to control.
The method they use to do this is unknown, and all attempts to protect or isolate the president(s) and other officials have failed.
The obvious decision would be to form a government/body that operates secretly, using leaders who cannot be identified easily. It is not known how the anonymous organisation identifies their victims remotely, so ideally all details including name, face and genetic origin of the leader(s) should be kept secret.
The objective of this body is to ensure the survival of the American people long enough until the threat is thwarted (and this could take years). This survival may or may not require management of numerous other institutions such as courts, army, banks, etc. as well as major policy decisions such as economic policy, and how money is used. What is essential in the existing infrastructure and what is not is for this government to decide.
(a) What kind of structure should this new body adopt to be more stable? Would a single dictator be better, or perhaps a communist government with no single head of chain of command?
(b) What would be the steps that have to be taken by the surviving government officials and administrative bodies to establish such a government?
(c) And how effective would it really be at governing the country?
P.S. I am aware this government will necessarily be undemocratic and somewhat unstable.