I'm thinking the Greeks, the guys who came up with democracy in the first place - albeit with slaves and sexism and a whole raft of other stupidity - they had a good idea when it came to determine the president of the Senate - lottery.
We already do this very well with the Jury Duty system.
Schools would prepare students.....
Imagine something like this (well - there are details)
At age 21 all U.S. Citizens are put into a pool, like the draft pool of old.
For all of the lowest level officials, like town select(wo)men and city council(wo)men, names are chosen from the pool by lottery. Those selected move into office & are then part of the second level pool.
For the second lowest level officials, names are chosen from the second level by lottery. Those selected move into the 3rd level pool.
For the 3rd level officials, names are chosen from the 3rd level pool, and so on all the way up to POTUS.
Any official found guilty of any kind of corruption at all is kicked out of all pools. National TV cheers the winners in their well-known stupifying way, but it works to keep the incentive to NOT CHEAT.
Each time your name is NOT chosen at a certain level, a copy of your name is added to the pool, increasing the odds that you will be chosen next time.
Depending on how many levels there are, the POTUS will be someone experienced and unbought.
It's a combination of anarchy and meritocracy. BUT there's no more of the CRAP CRAP CRAP of election commercials or robocalls. Big Business cant do *ANYTHING* about the process other than make fraudulent lotteries. And those are easy to catch. Oh, the gnashing of their teeth.
Never happen.