The Turnbull government's leading conservative cabinet minister - and a key architect of the same-sex marriage postal survey - believes the 'yes' campaign will win.

Immigration Minister Peter Dutton made the prediction on Wednesday night, just four weeks after the first ballot papers were distributed to households across the country, and four weeks before voting closes.

"My judgment is the 'yes' vote will get up and it will be in the order of... whatever it is... but it will be a win for the 'yes' vote and that is my judgment of where the outcome will be," Mr Dutton said.

The comment, made at an event in Sydney celebrating the Australian Financial Review Magazine's newly published power list, is significant because Mr Dutton led the push inside the cabinet to hold the non-compulsory, non-binding postal survey. He is also the first senior conservative cabinet minister to publicly predict a majority of Australians will support amending the Marriage Act.