The survey, carried out by NFO System Three, asked 1,033 people to attach a priority to 21 key policies on a scale of 1-10.
The least popular policy by far, categorised as "should never be done", was tuition fee hikes - 46 per cent took this view. The next most unpopular policy was congestion charges for drivers, with 34 per cent vehemently against.
Tuition fees are "the all-time stinker", according to Brian Taylor, BBC Scotland's political editor. Opposition is, uniquely, simi-larly strong among all age, gender and social class groups.
The Labour and Liberal Democrat coalition parties will note with interest that the most implacable hostility comes from first-time Labour voters (50 per cent, while the Liberal Democrats show 44 per cent aversion).
Other voters record similar levels of opposition, while women are more likely to be against (51 per cent say higher fees should never be introduced compared with 41 per cent of males).
Other findings suggest that the battle to win over public opinion in favour of cuts in class sizes could strike a chord with the electorate - "middle ranking among the priorities with little overt hostility", according to the BBC. Some 19 per cent made it their top priority, with another 31 per cent saying that it was among their top three issues for action.
This will please the SNP in particular which is calling for a phased reduction of sizes from 30 to 18 in P1-P3 classes. But Labour has already countered this stance, setting greater store by limits in maths and English classes in S1 and S2.
This week the Scottish Socialist Party pledged to aim for maximum class sizes of 20 and 16 in practical classes within five years.
But the issue given the highest priority, by 27 per cent of those who took part in the poll, was opposition to the use of private capital to build schools. Another 31 per cent cited public sector funding for schools as their second and third most important policy.
Among Labour and Liberal Democrat voters, 65 per cent ranked preference for publicly funded school buildings among their top three priorities; for the SNP, it was marginally above at 67 per cent.
There was significant support for an alternative, vocational curriculum for pupils aged 14-plus (56 per cent said it was among their main three priorities). But phasing out public funding for Roman Catholic schools was a top priority for only 23 per cent, while 21 per cent said that it should never happen.
Leader, page 28