The concept: A cafe (or another similar public establishment) where every visitor can get access to the sound system and pick their song of choice to be played through the speakers. The sound system is not divided to uniquely accommodate different rooms, tables, etc., so whatever you'll pick everyone in the cafe will be listening to.
The details: The trick is to divide the availability to control the sound system equally amongst all people in the cafe. After playing your song of choice you'd have to wait until all others had their chance to play something and your turn came back again. The degree of your availability would depend on how many people are in the cafe at the given moment and how many of them are willing to use their right to control the music.
I think the best way to go about this would be by using a request-based model - whenever you felt willing to play your song of choice you could request the system to do so, it would then show you how many people are already in line and when your turn will come, it would additionally notify you just before your turn to pick a song. At times where there would be no requests, the system would pick something automatically itself until the request comes.
On a technical level this would take implementing a computer into each table present at the cafe that the customers sit at. Baristas should also have the possibility for their equal input in this. The screen could be a part of the table surface, covered with safety glass so that you could put things on it, but be sensitive to the touch at the same time to enable interactions from the users. Having additional means of input (apart from the touchscreen) is a good idea - like a keyboard and mouse in a drawer under the table.
You'd be able to log in to your personal account on spotify, youtube, other music streaming platforms and play songs from your personal playlists or simply search for anything using the search function. The system would log you off and delete your data automatically when leaving the table.
The system could and perhaps should also have some basic Dj'ing features like overlapping two different songs, beat matching, volume fade in and out, etc., so that people who are familiar with these functions could use them and make the experience even better for everyone. A simple guide on how to use them would also be presented by the system so that the people willing to learn could do it and try them out in practice. Even if you ruined the music once or twice by trying to learn something this wouldn't be a big deal since you wouldn't get the chance to do it so often.
Another cool feature would be to highlight the table which picked the current song either in a physical space (by lighting it up, make it blink, etc.) or within the digital system (on each computer monitor). The first option seems like more fun, but the last one is more private which most people would probably prefer. There could also be an option to totally hide that the song was picked by you. However, to prevent people from randomly playing anything and messing with the system for fun just because they can I think publicizing which table picked the song as a mandatory feature is a good idea. It also encourages social interactions.
I think enabling a feedback system is also a good idea, people could vote whether they like the song that you picked or not and you could try something different accordingly if you wished to improve in that regard. If your table was highlighted while playing the song, this would encourage more live feedback and interactions from nearby tables. There could also be an option to give your turn to play a song to someone whose songs you enjoyed enabling that person to play more songs of their choice in a row.
Benefits that this idea brings: Good business model to attract customers. Less need to worry about adapting the music to the generalized taste of customers, cause they'll have the means to do it themselves. A test model to approach collective Dj'ing, where everyone participating in the listening of music/dancing can also contribute to what is playing, instead of one person being responsible for all the music or using a totally autonomous system. A good way to break the social ice and get unfamiliar people to start communicating with each other.
If such a system was proven to be successful/desirable it could be implemented in various places, not only cafes or other commercial indoor spaces where people gather but also free ones like public squares, shopping mall passages, libraries, parks, etc.