Most commentators in the press and from the Labour party have assumed that the Conservative-Liberal Democrat coalition government will be plagued by internal dissensions in the House of Commons. In fact, Patrick Dunleavy argues that the government can survive untouched until 84 right-wing Conservative MPs abstain, or 41 Liberal Democrats vote with the opposition – which should never happen. If the leaders and ministers can hold it together between themselves, this looks like a full-term government.

In a previous blog I explained the concepts of power index scores, and looked at some of the problems with this approach that have lead critics to develop an alternative approach, the influence-index. The influence index is an average of the immediate power score, plus the resources weight (in Parliament, the percentage of all MPs) that each actor has: resource weights reflect longer-term power, while the power index is very immediate and short-term.

The Table below shows how the power index and influence index apply to the 2010 Parliament (for more details see my previous blog). The Conservatives are the most powerful party, but with much less power than their share of MPs, The Liberal Democrats tie with Labour for second place in power terms. The smaller parties (the Scottish and Welsh nationalists, the Northern Ireland parties and the solitary Green MP) have small but disproportionate influence. This finely balanced situation will still apply throughout this Parliament on free votes, or on votes that are exempted from the coalition agreement.

Before the Coalition: Power and Influences Score with separate Conservative and Liberal Democrat parties, giving ten blocs in all

Now, however, everything has changed. Power and influence scores are highly sensitive to blocs coalescing with each other and hence to falls in the total number of blocs that are competing with each other. So when the largest and third-largest blocs (i.e. the Conservatives and the Liberal Democrats) coalesce into one bloc for most voting purposes, thus reducing the total number of blocs to nine, we can expect to see big changes. And my second Table shows how dramatic these in fact are.

After the Coalition: Power and Influences Score with a single Conservative-Liberal Democrat bloc, giving nine blocs in all

The Cameron-Clegg coalition government has a clear majority in the Commons, and as soon as any bloc gets past 50%+1 the power index assigns it total power, and gives zero power to all the opposition blocs. Put another way, the power index kind of gives up as soon as anyone becomes a winning bloc, which is one of the most important charges that its critics lay against it.

But the influence score keeps on working, because we can still average the power of a bloc and its resource weight. (We can in principle average it in many different, weighted ways: but for simplicity here I assume that we just take the mean of the two scores). On this basis, the Cameron-Clegg government has more than three quarters of the total power in Parliament, with Labour a long way behind on a fifth, and the small parties sharing less than 2 per cent of power between them.

At this point most media commentators have waxed lyrical about the disruptive potential of any ‘awkward squad’ MPs on the Conservative right. But the Tory right are highly unlikely to vote with the Labour party on many things, so that the most they can do is abstain. The maths of the situation show that a massive 84 out of the 307 Tory MPs will need to abstain before the government could lose a single Commons vote – which seems highly unlikely to happen. And even at this stage, the government would be the largest actor, and its power score would not be dented greatly. Not until the government faced 100 abstainers would its power score fall below half.

What about MPs on the left of the Liberal Democrats though, perhaps responding to party members who are anguished by the loss of centre-left credentials? These dissenters could surely vote with Labour, thereby swelling the opposition ranks as well as depleting government support. But it would require 42 of them before the government is at all imperilled – that is, nearly three quarters of the Liberal Democrats MPs before losing any vote.

Finally, the government can probably rely on the eight votes of the Democratic Unionist Party for most of the time, so that its insulation from defeat is even greater than I have allowed above.

In other words, the Cameron-Clegg coalition looks remarkably strong in Parliamentary terms. It is certain to go whatever distance the two leaders and two sets of Cabinet ministers want it to go. They’ve made a great start already, busting paradigms in all our thinking about British politics. Their formal agreement says five years, and they will probably need that long to make the austerity cuts, weather unpopular times, and come out on the other side. So pencil in May 2015 for the next general election.

And if you are in the Labour party, prepare for a long and frustrating opposition. Also, at the end of that time, if the coalition is still in being, a 2015 election under anything less than a fully proportional electoral system (that is, under first past the post or AV) could easily spell a new electoral disaster for Labour. Time to adjust mindsets all round.