A majority of voters oppose the bribery of people smugglers, today’s Essential Report reveals, with more than a third of voters strongly disapproving of the government’s payments to people smugglers to take asylum seekers back to Indonesia.

After revelations Australian officials secretly bribed people smugglers to return 65 asylum seekers to Indonesia, just 29% of voters approve of the bribes, with 56% disapproving, including 33% of Liberal voters (48% of whom approve). Although Labor (74%) and Greens voters (80%) have high rates of disapproval, 61% of “other” voters also disapprove. Only 25% of women approve, compared to 34% of men.

Essential also has some figures on the strong demographic differences between Australians on the issue of same-sex marriage (repeating a question it asked in early June, when voters split 59%-30%).

Previous polling has shown women are more supportive than men of same-sex marriage; there is also a very large age gap on the issue, with under-35s overwhelmingly supporting same-sex marriage and over-55s nearly split evenly, although more older voters now back same-sex marriage than oppose it.

Asked about their strength of belief on the issue, opponents of same-sex marriage were more likely to declare themselves “very strong” on the issue — 46% compared to 37% of supporters of same-sex marriage. That suggests, with opposition falling, the remaining opponents are increasingly composed of a diehard rump who won’t change their views. Forty-six per cent of Labor voters and 48% of Labor voters say they held their views on the subject strongly, compared to 31% of Coalition voters; the latter were more likely to hold strong views against same-sex marriage, while Labor voters were more likely to hold strong views for.

However, there is very strong support from all voters for a conscience vote on the issue in federal Parliament. On whether political parties should treat the issue as one of personal conscience or party policy, 58% of voters say conscience — including 65% of Labor voters, 55% of Liberal voters and 68% of Greens voters. Just 19% believe it should be a matter of party policy. Support for a conscience vote is higher among supporters of same-sex marriage than opponents.

On voting intention, what had looked like some recent momentum for the Coalition has stalled for the moment. The Coalition primary vote has surprisingly dropped a point to 41%, having steadily built up from its February nadir of 39% to 42% last week. Despite a bad week for Opposition Leader Bill Shorten, Labor remains on 39% and the Greens on 10% for an unchanged 52%-48% two-party preferred outcome in favour of Labor.