Two-thirds of voters support Labor’s proposal to slap a punitive tax on tobacco in order to deter low-income earners from smoking, today’s Essential Reports shows, while the biggest concern about the tax system is the wealthy and corporations not paying their fair share.

Labor last week proposed a massive tax hike on tobacco with the intention of stopping low-income earners from smoking by in effect pricing it out of their reach: 67% of voters back the proposal (including 39% who strongly support it), while 24% oppose it. Moreover, voters are virtually indistinguishable on the issue across party lines — 67% of Labor voters support it; 70% of Coalition voters; 67% of Greens voters and 72% of other voters.

Voters are evenly divided on whether the tax system needs a fundamental overhaul (41%) or relatively minor changes (39%), but they are clear on exactly what bothers them most about tax: 59% of voters say “the feeling that some corporations don’t pay their fair share” bothers them a lot, while 54% say “the feeling that some wealthy people don’t pay their fair share” bothers them a lot. In comparison, just 23% say the amount they themselves pay in taxes is what bothers them a lot. Coalition voters are a little more relaxed about the tax system — 20% say the amount they pay in tax bothers them a lot, compared to 26% of Labor voters, while 54% of Liberal voters say corporations not paying their fair share bothers them a lot, compared to 62% of Labor voters.

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This annoyance regarding high-income earners and corporations is reflected in broad views of the system: voters believe the tax system generally isn’t very fair. Just 4% say it is “very fair”; 36% say it is “moderately fair”, while 30% say the tax system is “not too fair” and another 22% say it is “not fair at all”. Coalition voters were more likely to find it “moderately fair” (46%) and less likely to declare it “not fair at all” (15%); high-income earners are also more likely to find the system fair, especially when compared to low-income earners.

But when it comes to personal fairness, the similarity between Coalition voters and high-income voters disappears. High-income earners are more likely to complain that they pay more than their fair share of tax than others (47% of high income earners, compared to 40% of all voters and 25% of low income earners); but Liberal voters and Greens voters are more likely to say they pay about the right amount of tax (43% and 46%, respectively) than Labor voters (31%).

Meanwhile, Malcolm Turnbull’s leadership appears to have begun turning around voter perceptions of his party. In October, we saw that his ascension had improved the Liberals’ standing on some issues but not others, but now the party’s performance on different policy issues is improving across the board. The party’s lead over Labor as the best party on economic management has increased from 18 points to 21 points; it is now level with Labor on health, an improvement of five points since October; it has cut Labor’s lead on education from seven points to one point and Labor’s lead on industrial relations fairness from eleven points to six points. The Liberals now lead Labor by 22 points, up four, on “political leadership”, and on two issues thought to be strengths of Tony Abbott they have also moved ahead under Malcolm Turnbull. The Liberals’ lead over Labor on treatment of asylum seekers has increased from seven to 15 points and, despite agitation from Abbott loyalists for an invasion of Syria, its lead on security and terrorism has gone up a point to 23 points.

That appraisal, however, hasn’t translated into voting intention: the Coalition and Labor both remain unchanged on their primary votes — 44% for the Coalition and 35% for Labor — while the Greens have lifted a point to 11%. The two-party preferred outcome has fallen to 51%-49% in the Coalition’s favour.