The Australian government has, notoriously, decided to run what it calls a plebiscite on the question of marriage equality in Australia. It will put up a bill to set up the running of the plebiscite as a mainstream vote, but this is expected to fail. Its fallback position is to have the Australian Bureau of Statistics (‘ABS’) run a voluntary postal vote.
On a straightforward reading of the relevant statutes, it is unlikely that the ABS is empowered by its legislation to run the vote. The former head of the ABS appears also to hold this view.