MELBOURNE, Australia — The Australian government’s highly contentious proposal to put the question of same-sex marriage to a nationwide postal vote is legal and may proceed, the country’s High Court ruled unanimously on Thursday, eliminating the last hurdle before ballots are to be mailed out next week.

The survey — which is voluntary, unlike in-person elections in Australia — was challenged in two separate cases brought by advocates of same-sex marriage and members of Parliament. Run by the Australian Bureau of Statistics, the vote will be unique in Australian history: Nothing in the law requires it to take place before Parliament may act, and lawmakers are not bound by its results.

Though the court has announced its decision, it could be weeks before it releases the reasoning behind it. Legal experts suggest that the core argument was whether the government unlawfully appropriated funds for the postal vote without parliamentary approval. The government used an appropriations clause that allows its finance minister to spend up to 295 million Australian dollars — or around $236 million — if the expenditure is “urgent” or “unforeseen.” The plaintiffs’ case against the government centered on those two words, claiming that the postal vote did not fulfill either obligation.

“That’s really the core argument — whether this can nonetheless be authorized by this other provision,” said George Williams, dean of law at the University of New South Wales. “The High Court has said that the federal government can’t spend taxpayers’ money without the approval of Parliament,” he said, referring to another recent decision by the court. “The government twice sought that approval for a national plebiscite, but Parliament rejected those attempts.”