Very interesting idea, there must be some SciFi works on this subject.
Would the ePresident be fixed for their term of office (no upgrades whilst in post)? Could you ask it questions as a citizen before voting to know how it would respond for any given parameter set? Would it be programmed according to the Three Laws?
Perhaps all parties could submit an ePresident candidate and each could get a vote on all actions based on the proportion of the population who voted for it.
The compiled version might be different. A solution would be to allow everyone to run a local copy of the president which gets the same data-feed so it would respond the same in all instances. The problem is of course that a president deals with confidential information which you don't want to just broadcast over a network for anyone to see.