When a politician elected with maybe 40% of the popular vote, from the 65% of people who vote, gets a 51% advisory mandate from those few who show up to vote in the referendum, it's a pretty weak reason to drag everyone else along. Democracy is built on the idea of false consensus. That once enough people decide on something that it doesn't matter if others do. The closer we go to simple-majority, the worse that is.
fwiw, I find it funny that you think that's conservative. I get more feedback that it's hyper-liberal. I don't think either are correct.