As the media searched for a narrative around the public response to last week’s federal budget, two major opinion polls published on Monday appeared to offer only confusion.

In The Australian, Newspoll found a government that trailed miserably for most of 2017 was within striking distance, facing a two-party deficit of just 51-49.

But in the Fairfax papers, an Ipsos poll suggested the Coalition was as badly placed as ever, crediting Labor with a commanding lead of 54-46.

Take a step back though, and it becomes fairly clear that this was a well-received budget that has nonetheless failed to make a measurable difference to voting intention — so far, at least. Newspoll and Ipsos were actually more or less agreed on the Labor primary vote, which Newspoll had at 38% and Ipsos had at 37%.

However, Newspoll came in stronger for the Coalition, at 39% rather than 36%.

Converting these numbers into the two-party totals that make the headlines had the effect of widening the gap, partly due to Newspoll’s newly adopted formula for allocating minor party preferences. As discussed here recently, this appears to involve giving the Coalition around 60% of One Nation preferences, rather than the 50% they received in the handful of seats they contested in 2016 – enough to boost their two-party result by around half a point.

Ipsos’s concession to the possibility that preferences may not behave as last time is to publish a separate result based on how respondents say they will allocate them, and this landed closer to Newspoll at 53-47. Rounding must also have been a factor, as Newspoll’s primary vote numbers look more consistent with a 52-48 result than a 51-49.

Throw Essential Research’s 52-48 result into the mix, and it seems likely that the Coalition came in too low from Ipsos this time around; that they may nonetheless be doing a shade less well than Newspoll suggested; and that the budget hasn’t made much difference to the equation one way or the other.

This is not to say voters are indifferent to the budget, which all three pollsters have found to have been positively received. Most instructive are the findings from Newspoll, which has helpfully maintained a consistent line of post-budget questioning back to the late 1980s, a period encompassing 17 Coalition and 14 Labor budgets. Paul Keating’s contention that Peter Costello “got hit in the arse by a rainbow” sits well with these results, with the budgets of 2004, 2005, 2006 and 2007 standing apart in the positivity of their perceived impact on personal finances.

Now we have a fifth budget that can claim the distinction of a net positive result on this measure, albeit just barely (29% to 27%, with the rest uncommitted).

The failure of a seemingly popular budget to deliver on voting intention is a tale familiar from Costello’s time, when two rounds of tax cuts in the Howard government’s final year did little to shift the needle away from Labor.

Fairfax’s Peter Hartcher dipped into the political science handbook to propose this as evidence of “sociotropic” voting, whereby voters ask not what tax cuts can do for them, but what they can do for their country.

However, this is complicated by Newspoll’s long history of showing voters make only a limited distinction between a budget’s impact on the broader economy and its impact on them personally.

Budgets invariably score better on the former question than the latter, but the two are highly correlated (notwithstanding outliers like Peter Costello’s debut budget in 1996, which evidently impressed voters as tough but fair — a feat Joe Hockey singularly failed to replicate in 2014).

There is no better example of this than Costello’s final budget in 2007, which scored the best results over three decades of Newspoll on both measures, without yielding the electoral dividend anticipated by the sociotropic model.

The latest polls do offer encouragement for the goverment, but it does not lie in the budget response measures, which only appear to have been consequential in the disastrous cases of 1993 and 2014. Rather, the good news is to be found in a strong uptick in Malcolm Turnbull’s personal ratings — and here at least, Newspoll and Ipsos are singing from the same song sheet.

If the historic tendency for prime ministerial approval to serve as a leading indicator for voting intention is any guide, Malcolm Turnbull may finally be in a position where he can await new opinion polls with hope rather than dread.