If Vancouver had a referendum to get rid of bike lanes and ban bikes from streets entirely, I doubt you would be saying the same thing. There are far more drivers than cyclists. I guess in that case all the drivers should vote to get rid of bike lanes and ban cyclists?
Right, because global referenda which mainly affect a minority are examples of democracy?
Should gays be allowed to get married? Let's hold a referendum! Should some natives be given back a piece of land? Let's hold a referendum!
For the record, I currently sometimes ride where bikes are banned, namely certain sections of certain highways. So I wouldn't care. And I'm not a big supporter of bike lanes.
I'm not opposed to the idea, however, of requiring cyclists to be licensed somehow as a requirement for the use of public roads that carry motor vehicles. Don't ban; qualify.
If everyone voted for just the things that helped them and against everything else - whether in referendums, elections, whatever - minorities would pretty much always be repressed.
If someone thinks that a city council whose main focus is getting rid of bikes is the best for them, they should absolutely vote that way. The idea that I would have someone vote for what she thinks is good for me rather than him or herself is absurd.