In my ideal system, we would propose some sort of inherently progressive tax at some fixed %, and say that the basic income was “however much that produces, divided by everybody”. That means that as the economy grows, the basic income increases. At the beginning, the basic income might not really be enough to live off of (especially if I got my calculations wrong). As we get more things like robot labor and productivity increases, so does the income. By the time robots are good enough to put lots of people out of work, they’re also good enough that X% of what the rich robot-owning capitalists make is quite a lot, and everybody can be comfortable.
Then various Congresspeople can debate at what point the UBI is large enough that we can eliminate various welfare programs. On the one hand, welfare programs can be sticky, so we might worry they would be overly cautious. On the other hand, many Congresspeople are Republicans, so they probably wouldn’t be.