Recent revelations of corruption within individual trade unions has done little to damage perceptions of the importance of unions to working people, new polling from Essential Research shows. And voters are broadly happy with Prime Minister Tony Abbott’s choice for Governor-General, Peter Cosgrove.

Some 61% of voters believe unions are important for workers, compared to 30% who believe they’re unimportant. That’s up from 57%-34% in December, despite media stories about corruption on the part of Construction, Forestry, Mining and Energy Union officials and the government suggesting there was a need for a royal commission into unions. Liberal voters don’t share the view — only 44% believe unions are important for working people, compared to 50% who say they aren’t. Overall, 45% believe workers are better off when unions are stronger, compared to 27% who think workers are worse off; this is up from 43%-29% in May last year. For Liberal voters, 46% believe workers are worse off when unions are strong.

On the selection of Peter Cosgrove, 30% of voters say he’s the best person for the job; 34% say he’s a good choice; 11% say he’s “acceptable” and only 4% believe he’s a poor choice. Liberal voters are most enthusiastic, with 46% saying he’s the best person for the job. Greens voters, however, are unenthusiastic, with 15% saying he was a poor choice and 21% rating him as “acceptable”. Cosgrove also appears to be the choice of the old — 79% of voters aged over 55 believe he’s a good or excellent choice, compared to 45% of those under 35.

Essential also asked voters about the method of selection of the governor-general. Some 43% support the role being appointed by the government while 40% want the role to be elected by voters. Older and Liberal voters more strongly prefer the role being appointed.

There’s also an interesting age divide on the question of paid parental leave. Voters continue to prefer the existing paid parental leave scheme established by Labor over Abbott’s “Rolls-Royce” scheme, 36% to 23%, and even Liberal voters are nearly evenly divided on the plans, with 28% supporting the Abbott scheme and 26% preferring Labor’s. But voters under 35 prefer the Abbott scheme 36% to 35%, while older voters, including over-55s, prefer Labor’s scheme by big margins.

Essential last week also repeated questions on the incidence of intolerance in Australia asked in 2012 and 2013. Perceptions of racism as “large” or “moderate” problem in Australia fell from 69% in 2013 to 64%; religious intolerance fell from 54% to 51% and homophobia from 51% to 47%. But perceptions of ageism as a “large” or “moderate” problem increased from 46% to 49%, and sexism only moved from 52% to 51%. Women are far more likely to see intolerance as a significant issue, being more likely than men to believe racism, sexism and homophobia are problems, Labor and Greens voters are more likely as well; older voters are more likely to see ageism as a significant problem.

Some 36% of voters say they’ve witnessed or experienced racism in the past year, which is down from 39% last year, but sexism has stayed the same on 29%, with 33% of women saying they’ve experienced it or witnessed it; the proportion of voters who have experienced or witnessed homophobia has edged down from 26% to 24%. Younger voters are also more likely to have experienced or witnessed all forms of intolerance except ageism than older voters.

On voting intention, both the Coalition and Labor have improved in the last week, with the Coalition picking up a point to 43% and Labor picking up two points to 38%. The Greens are down one to 8%; the two-party preferred outcome remains at 50:50.