Your individual stations wouldn't be on the blockchain... just the public stations.  Think of the public station as 'broadcast radio'  where as private stations are like pandora.   The software on your local computer would perform the calculations to find similar songs and play them for you.

So my personal station could just play the songs which haved been broadcasted by the pubic station after I have voted up the song. If not, people would have no incentive to vote up songs on blockchain. Am I right?