Analysis: There's been much talk of moral authority. But in the horse-trading now at play in deciding the future of Scottish government, morality is the least of their concerns. After the eye-wateringly tight results on Friday, democracy is about something much simpler - arithmetic.

There's been much talk of moral authority. But in the horse-trading now at play in deciding the future of Scottish government, morality is the least of their concerns. After the eye-wateringly tight results on Friday, democracy is about something much simpler - arithmetic.

The key to Holyrood power is the number 65. Government authority comes from the party leader who can command at least that majority of votes in the chamber of the Scottish Parliament.

That figure assumes the opposition's ability to unify against those in government, and that could make opposition-building as important as coalition-building. Alex Salmond merely needs to get more in favour of his nomination as First Minister than against, with abstentions potentially crucial to deciding the future of Scotland.

If LibDems or Tories sit on their hands, he could be in. But he also wants a majority to secure a vote for his ministerial team and for his budget and legislative programme over the next four years. That includes an independence referendum, to which a clear majority of MSPs are firmly opposed.

While Tories have ruled themselves out of coalition, LibDems spent the weekend licking electoral wounds. Some think the answer is to retrench in opposition, and build a clearer identity.

But going backwards, being out of power and being fourth largest group is no way to achieve anything. That is why LibDems want to stay in power, but not with Labour, even if talks with the SNP collapse.

Their best hope of growth now is to benefit from continued Labour decline, rather than seeking to prop up their partners of the past eight years.

Despite LibDem setbacks, they last night stood firm against an independence referendum. Arithmetic has strengthened their hand. On that crucial issue, Alex Salmond can count on his own group, and probably two Greens.

While his group grew, it did so at the expense of 11 Socialists and Greens who supported independence. So while the SNP leader has 20 more MSPs, independence has only nine more supporters than before.

Counting on only 50 pro-independence votes out of 129, when the others are implacably opposed, means a referendum cannot happen.

If the SNP leader went for a minority administration, he could be sure of the challenge of learning the ropes of government, the hassle of cobbling together majorities for each week's votes, while facing flak from Whitehall, and he would still not get a vote on independence.

The choice is between being in power with no referendum or being out of power with no referendum. It is not a difficult choice to make.

Jack McConnell faced a similar problem over reform of council voting four years ago, when the LibDems knew a Holyrood majority could vote it through whether the Labour leader was in or out of coalition.

If Mr Salmond accepts that arithmetical reality and can explain it to his own party, the SNP and LibDems can argue over spending priorities, onshore wind farms (LibDems want lots more, the SNP want them limited) and, of course, ministerial posts.

If Mr Salmond fears Labour's ability to unite the opposition against him, he would still need the two Greens to reach 65. Patrick Harvie and Robin Harper hope they can return to previous strength through having a role in government.

They prefer to offer conditional stability, meaning they would back the First Minister and his budget, but force him to persuade them for other votes.

What price would they demand? The M74 extension through Glasgow could be in trouble, as could the Aberdeen ring road. Greens are sceptical about the need for another Forth crossing, and they want to stop airport expansion.

If this coalition is to fly, it will need carbon neutral fuel.