One-third of people believe the next Senate should have more or the same number of crossbenchers, according to polling done for the Australia Institute, a progressive think tank. This compares with 28% who would like to see fewer.

There was a big divide along political lines. More than half (52%) of Coalition voters wanted fewer; only 23% wanted the same number or more. Some 42% of Labor voters favoured the new Senate having the same number or more; just 16% wanted fewer.

The expectation is that, despite the changes in the Senate voting system which work against “micro” players, a substantial number of non-Green crossbenchers will be elected to the new Senate, including about three from the Nick Xenophon Team.

The national poll of 1,437 people was done between May 23 and June 3 through Research Now.

The role of minor parties and independents has come into focus in the campaign with Malcolm Turnbull at the weekend appealing to people not to lodge a “protest” vote. The prime minister warned of the “chaos” of a hung parliament.

Newspoll is showing a rise to 15% in support for “others” – independents and parties other than the major parties and the Greens.

In the poll, people were told that in the parliament just finished the government had to seek the support of crossbench senators to pass legislation – they were asked whether this was normal or unusual for Australia. More than half (52%) said it was normal, 24% said it was unusual and 24% did not know.

People were also asked about particular decisions by crossbench senators, who sometimes voted with Labor and the Greens and sometimes with the government.

Some 41% supported the crossbenchers voting to block university fee deregulation (30% against); 44% backed their voting to abolish the carbon price (30% opposed); 37% supported their stopping plans for the young unemployed receiving payments for up to six months – less than the 40% who opposed. Nearly four in ten (39%) opposed their decision to abolish the mining tax (33% supported). People overwhelmingly (69%) supported their voting to keep renewable energy funding, with only 13% opposing.

Most people supported at least three of the crossbench decisions asked about and 85% supported at least one.

The Australia Institute’s executive director, Ben Oquist, said the polling results indicated prime ministers were more hostile to the Senate than the public.

“While governments often criticise the Senate, its constitutional role is to block or amend legislation as it sees fit,” he said, and the public’s attitude to the crossbench seemed to accord with this. “Indeed, a Senate not controlled by the government can be a help. It’s a bit like ballast in a ship – a government that uses it well gets smoother sailing, a government that handles it badly gets sunk by it.”

Meanwhile, independent senator Nick Xenophon, who expects his team will win three Senate spots in South Australia, on Monday played down the prospect of a hung parliament. “I think it’s highly unlikely … I can’t see that the Coalition will lose 15 seats and then be put into a hung parliament situation.”