However, in ancient Athens, one could become a magistrate (~a small-town mayor in modern times) through random selection. There was a term limit of one year, and you were only allowed to serve once in a lifetime. You also had to go through a basic examination called the dokimasia to be deemed competent.
Several other civilizations have used this method over history, typically with the intention of preventing corruption. https://en.wikipedia.org/wiki/Sortition
The people in legislative positions have a lot of power and there is no way to prevent that since the whole point is for them to have power to run the country.
Thus, it inherently attracts the sort of people who crave power and influence, which is exactly the sort of people who should not be allowed to have it.
So the only solution I can think of is to make it impossible to actively seek those positions of power, by assigning them randomly.
Why would they have any incentive to do a good job?
Also, why would they have any desire?
Also, that seems like a lot of money. >95% of people would be happy with the $1M per year salary.
If you're selected for public service, then you're expected to do good for the country, and not just a specific monied interest. And that means not having to worry about money ever again. You win capitalism. Done. Have fun. Live your life.
That could also be done with annuities so that they get a "allowance" each month until dead.
If you have a system in place that can find and punish bribes - why not pay them a reasonable amount of money - and just eliminate bribes without spending $0.1T per year...
Famously, Singapore maintains a very effective, clean civil service by paying market rates, and sometimes for some ministers that is actually millions of dollars a year.
Your worth should be based on your skills (meritocracy) - not by winning the lottery and how much people will pay to influence you (luck).
And with deciding "merit" are the kingmakers, or the "meritmakers".
Congratulations. You now have created a new class of people who can take bribes and subvert leadership under the term "merit".
And, explain how one would calculate "merit"? In my experiences, meritocracies are monocultures that put forth their own biases as "merit".
1: money isn't the only form of bribery.
2: people who want more... will always want more and will never stop taking.
3: there is no good way to tell a person from someone who wants to give to help, and someone who wants to give to get something in return.
A more effective if morally dark methodology is publicly and viscously execute people who take bribes in this system.
As it is, I'm not sure the billion does anything other than ensure that the one policy absolutely every randomly-appointed political figure from the vague woolly liberal to the literal neo-Nazi agrees upon is zero inheritance tax...
I actually think it's a wonderful thought puzzle at the least.
The two problems I have with it though, are reflected in Lincoln's 1st inaugural address:
* His criticism of the idea that only the Supreme Court can determine constitutionality: the instant they are made in ordinary litigation between parties in personal actions the people will have ceased to be their own rulers, having to that extent practically resigned their Government into the hands of that eminent tribunal
* His assertion that rule by a minority leads to tyranny or despotism.
If the thought puzzle could be extended by substituting the current closed party primary system with random selection initially - but still have a general election to choose among those candidates, you might find a way of creating a random-democracy hybrid.