Governing is painful; coalition government even moreso. To govern is to choose, after all. Prioritising issues and policies over others means someone is going to be rejected and disappointed. Those choices become that much more difficult in coalition government, involving tougher relationships and the rejection at times of your own party’s and voters’ preferences in favour of your partner’s.

In countries with majoritarian democratic cultures like the UK’s, we are used to the notion of ‘elective dictatorship’. If you campaign on taking the UK out of the EU and you win, you get to do it and there is virtually nothing that can be done to stop you. Right or wrong, if you stand and win on a manifesto, you implement that manifesto.

I think that because of this understanding, which is culturally ingrained as much as it is merely a feature of the system that governs us, we have a particularly hard time reconciling ourselves with the compromises that coalition governments entail.

Who can forget those heady summer days of 2010, when David Cameron and Nick Clegg joked with each other as they announced the first coalition government since the Second World War.

And who can forget how quickly the sweet taste of power turned to ash in the mouths of the Liberal Democrats, as broken promises and their embrace of austerity led to the party’s annhihilation at the 2015 election.

The Liberal Democrats’ experience fits a general rule that a coalition’s junior partners suffer more than the senior partner. A 2020 study of 219 elections between 1972 and 2017 found that junior partners in coalition governments – governments with junior partners holding ministerial office – consistently underperform both senior governing parties and opposition parties at elections.

In all of this, Scotland is an outlier. We had two Labour-Liberal Democrat coalition governments in the 2000s, neither of which led to the Liberal Democrats losing any significant amount support.

And now, we have a ‘coalition’ in which it is very much the senior, not junior, partner that finds itself the focus of ire.

The past couple of months have seen an intensifying drumbeat of SNP voices calling for the Scottish Government to scrap, renegotiate, or put to a vote of SNP members its cooperation agreement with the Scottish Greens, also known as the Bute House Agreement.

Those figures have been, it has to be said, the usual suspects, from Joanna Cherry to Fergus Ewing to Kate Forbes.

Sussing out the aggregate views of the SNP’s membership on the deal is tricky. SNP members overwhelmingly voted in favour of the deal in 2021, but its critics point to this year’s leadership election in which 81% gave a preference to Ash Regan, Kate Forbes, or both.

However, 71% gave a preference to Humza Yousaf, who vocally supports the deal and has stated that it will continue until the 2026 Scottish Parliament election, and who ultimately won that contest.

But it is clear that a chunk of the SNP’s voters are souring on the deal.

A poll released last week, conducted by Survation for the communications and policy advisory firm True North, found that net public support for the arrangement has fallen from -1 in May to -12 now.

Among the SNP’s voters, net support has fallen from +46 to +31, and from +39 to +17 among 2014 Yes voters. A quarter of both cohorts now oppose the deal.

As Professor Sir John Curtice articulated it last Wednesday, the Bute House Agreement has gone from being supported by the government’s voters and opposed by the opposition’s, which is to be expected, to being opposed by the opposition’s voters and by a growing chunk of the government’s voters as well.

So do the deal’s detractors have a point? Is the Bute House Agreement becoming a political liability, perhaps even threat, to the SNP and the Scottish Government?

Well, first of all, between those two polls support for the SNP was steady, and the SNP’s decline before the summer was primarily driven by its divisive leadership contest. The swing against the deal hasn’t directly cost them support in the polls.

Not yet, anyway, and to answer whether it could requires returning to the central puzzle of why, in this case, it is the senior and not the junior partner that is the target of ire.

Over December and January this year, the debate over gender recognition reform reached its vitriolic peak as polling showed that most Scots opposed the GRR Bill, and the issue dominated the headlines.

But the Bill’s popularity was not, I think, the real political problem for the SNP. The real problem was that the Scottish Government looked distracted. At the height of a cost-of-living crisis and facing serious challenges across myriad policy areas, half of voters believed that the Scottish Government was prioritising gender recognition reform.

Less than a fifth thought they were prioritising the economy. Whether that is fair or not is politically irrelevant – in politics, perception is reality.

Now consider the policy issues at the heart of the controversy over the Bute House Agreement: Highly Protected Marine Areas, the deposit return scheme, phasing out gas boilers and encouraging uptake of heat pumps have all attracted criticism and absorbed substantial media attention, with the Green Ministers’ faces plastered across newspaper front pages and TV news bulletins.

The popularity of these policies is neither here nor there. The fact is that these are not the priorities of voters. In the latest Redfield and Wilton poll, the overwhelming majority of voters say that the economy and the NHS are the most important issues facing the country.

And here lies the challenge and potential danger for Mr Yousaf. The longer it looks like he is choosing to put the Green’s policy priorities before his voters’, the longer the controversy over the Bute House Agreement will fester, the weaker he will look, and the greater the electoral danger.

The SNP need to get back on the front foot, get their junior partners off the front pages, and establish an ironclad focus on voters’ priorities.

That doesn’t necessarily mean scrapping the deal, but to govern is to choose, and Mr Yousaf faces difficult choices in the months ahead. If he wants to survive as First Minister past 2026, those are choices he cannot afford to get wrong.