It is election season in Puzzlevania. There are two candidates: the incumbent and a challenger. Of the $20$ million citizens, only $1$ percent support the current president; the other $99\%$ favoring the challenger.
Here's how the election system in Puzzlevania works: There is a list of numbers, $n_1,\dots,n_L$. The entire population is divided into $n_1$ equally sized groups. Each of these groups is divided into $n_2$ equally sized subgroups, each subgroup is divided into $n_3$ equal sub-subgroups, and so on down the line. On election day, each sub-sub-$\dots$-subgroup elects a representative to vote for it at the next level up. Tie votes count as wins for the challenger.
You can think of this system as a many-layered version of the American electoral college, where all states have the same population.
The current president has the power to choose the numbers $L,n_1,\dots, n_L$, and to choose which voters go in which groups. Can he do this in such a way that he gets elected?