This is the second in a series of posts in response to John Rentoul’s excellent article, much of which discussed the politics of our 11 July central seat forecast (Con 296, Lab 295, LD 31; so either Con+LD or Lab+LD would have a majority).

I have mixed feelings about speculation on the parliamentary arithmetic of any particular forecast. Part of the point of the forecasting method is to estimate uncertainty, which is naturally huge this far away from an election. As the below graphs show, there is a wide range of outcomes within the prediction intervals, so it arguably does not make sense to focus on just the central one.

However, I do think it is healthy for there to be more consideration as to how government formation would work under different plausible election outcomes. There wasn’t enough of this in the run up to the last election even though the polls and forecasters were suggesting a Hung Parliament.

So in that spirit I would like to add a couple of points to some of the discussion I’ve seen from John Rentoul and others.

First, while a Hung Parliament is highly likely, some kinds of Hung Parliament depend on very precise parliamentary arithmetic that is so fine as to be very unlikely. Last week’s forecast I think was one such case: the Liberal Democrats being able to choose between forming a majority (or even near-majority) coalition government with either of the two main parties. Very small deviations in the seat totals for any of the three main parties in any direction (except one) would change the politics significantly.

The exception is an increase in Liberal Democrat seats at the expense of both major parties. That would increase the Lib Dems’ king-making power. Conversely, if the predicted Lib Dem recovery from 9% in the polls to 13% at the election does not materialise then the Liberal Democrats may not have enough MPs to form a majority coalition with either of the two major parties.

What this discussion of parliamentary arithmetic does help illustrate is that the potential for the Lib Dems to be king-makers depends substantially on them having enough MPs. The more MPs the Lib Dems have, the more likely a Hung Parliament, and so the more likely they would get to choose which major party governs with them.

A second reason not to take any particular central forecast too seriously is that the forecasting methodology is not set up to consider deviations from uniform national change for UKIP. The local and European elections I think showed us that UKIP are developing pockets of strength that might be big enough to mount successful General Election campaigns from.

The 2010 UKIP vote was so evenly distributed across constituencies that UKIP need a national share of the vote much greater than their current 12% for a uniform change projection to give them a seat. But since they now have concentrations of strength it is reasonable to expect them to be able to win a few seats.

I’m not going to predict now how many seats UKIP will win in 2015, but anyone speculating on parliamentary arithmetic should bear in mind the possibility that UKIP will win sufficient numbers of seats to have implications for government formation. This might be partly because UKIP winning seats would increase the chances of a Hung Parliament and may make it more difficult to form a majority coalition government. There may also be indirect effects depending on who UKIP wins seats from.

So anyone pondering the parliamentary arithmetic of any particular seat forecast might do well to consider how the politics would change if UKIP won half or even a whole dozen of seats.