There have been many experiments over the years, as far as I know in Alaska, Utrecht (Netherlands) and Finland.
The one in Alaska is quite interesting actually and has existed since 1982.
The Alaska Permanent Fund is a state-owned investment fund established using oil revenues. It has, since 1982, paid out an annual dividend to every man, woman, and child living in Alaska. In 2015, with oil prices high, the dividend totaled $2,072 per person, or $8,288 for a family of four.Feb 13, 2018 -- Source: Vox
I hadn't thought about combining basic income with a voting system to allocate resources. I could totally see that being possible in the future. I think we might be experiencing a lack of available jobs relatively soon, due to automation.
The voting I was referring to above was voting with currency tokens. One person may decide to vote on a sports car by buying it with their basic income tokens, whereas another person may vote on public transportion by paying for it and then save more of their basic income to go on a trip. Someone else might give another person some of their tokens because they like hearing their jokes, etc. So the currency tokens are the votes that direct the robots and perhaps other humans on what is desired and what is valued such that we best price limited resources and know what to do with them. Giving a MBI in tokens would possibly reduce the human incentive to produce, but they would still create some of the same properties of a free market through the signals humans provide by buying things. However, even if robots take over most jobs, I still think there will be much for humans to do. For example, sometimes I enjoy purchasing things electronically without ever interacting with a human, but I also appreciate and desire businesses where I can get to know the owner and the employees. The personal touch by other humans is worth something to me.