Explanation:

1. Comptroller and Auditor General (CAG) - Cannot assume an office under the Government of India after retirement.
2. Chairman of the Union Public Service Commission (UPSC) - Cannot assume an office under the Government of India after retirement.
3. Chairman of the State Public Service Commission - The prohibition for holding office after retirement applies to offices under the government of the State they served in, but not explicitly under the Government of India.
4. Election Commissioners - Cannot assume an office under the Government of India after retirement.

So, 3 out of the 4 listed authorities cannot assume an office under the Government of India after retirement.