I'm sure some kind of Universal Basic Income (UBI) or central planning/rationing system will be the endgame for our economy, once robots completely replace humans. However, I've been having trouble imagining a system that can easily scale to accommodate both 25% unemployment, and also (theoretical) 100% unemployment.
The primary problem is thus: under 100% automation and UBI, all goods/services are paid for with tax money. If a productivity/income tax on the robot/business that creates/sells a widget (respectively) equals less than 100% of the value of the widget, then private business will gradually siphon money from the human side of the economy, leading to deflation. OTOH, if tax equals 100% of the value then gross profit is impossible, making it impossible for the business to grow or pay off loans used to make it grow. As I see it, at this point, established businesses would have to be nationalized in order to avoid breaking the economy. Each person with a college degree could be given some resources to experiment with a pet project or two, but otherwise resources would be spent according to consumer demand. Give some nice bonus to those who have a successful new business/invention and then nationalize it; hey that sounds like how patents and copyright are supposed to work. However...
Central planning, nationalization and UBI aren't feasible/easy with 25% unemployment because ~25% of purchases will be with tax money, and so ~25% of GDP will need to go back into taxes. The 75% of employed people (and businesses) will pay 1/3 of their income on average, as tax (who wants to take bets that lobbying causes businesses to pay less than average). As the permanently unemployed increase in numbers, this portion paid as taxes will increase, encouraging people to quit their job and live off the UBI, leading to a runaway effect, even if automation isn't yet ready for 100% replacement of humans. There will be cases where there is a point where it is too expensive to hire a human yet there is no robot capable of doing their job. For example, if all your needs were taken care of with the UBI, would you work full time for $15k/year (2016 dollars) doing unpleasant drudgery if 75% of that were taken as tax?
I suppose one could say "well, as an economic revolution, of course there will be hard times during the transition" but who's going to vote for temporary hard times? People would rather hang on tight to the status quo, watching the inevitable train crash come straight towards them in slow motion. History bears this out, as explained e.g. in the novel Collapse.
I predict nothing will change until many years after the point at which a difficult change would have been less painful than trying to hang on.