The belief that a Labour minority government reliant on SNP support would be dragged significantly to the left has hardened into conventional wisdom. Some, such as Len McCluskey, welcome this prospect, while the Tories and others issue dystopian warnings of a high-spending, high-taxing, high-borrowing administration that scraps Trident. Slightly embarrasingly for Labour, Peter Mandelson's consultancy firm Global Counsel has warned: "[The SNP will] pull the Labour party to the left, away from the centre ground of English politics. This will include pushing Labour towards higher public spending. In addition, the SNP will intervene in some high-profile policy areas, such as by attempting to block the replacement of the Trident nuclear fleet."

But as I've written before, the SNP's leverage is nowhere near as great as stated. In the case of Trident, those MPs in favour of renewal (most of Labour, the Tories and the Lib Dems) will far outweigh those opposed. As long as the Tories are prepared to walk through the division lobbies with Miliband, there is no chance of the SNP blocking defence spending (as its deputy leader Stewart Hosie has grandiosely suggested they would).

On fiscal matters, the SNP wouldn't drag Labour significantly to the left for the simple reason that isn't much to the left to begin with. As the IFS noted last week, the party's "stated plans do not necessarily match their anti-austerity rhetoric". The nationalists' commitment to ensure that the deficit and the national debt fall "in every year as a share of national income" means that they have less room for manoeuvre than assumed. Indeed, under some assumptions, the SNP would cut public spending by £5bn more than Labour over the next parliament. Ed Miliband and Ed Balls responded by emphasising that Labour wanted to deliver a surplus on the current budget, rather than merely balance it (which could entail greater cuts), but the gap between the two parties is still marginal.

In the case of tax, the SNP manifesto proposes "the reintroduction of the 50p top tax rate, a tax on bankers' bonuses, a bank levy, a mansion tax, a crackdown on tax avoidance, the abolition of 'non dom' status, reversal of the married couples' tax allowance, and a review of the pension tax relief available to the wealthiest." But every one of these measures is already supported by Labour. Indeed, it was arguing for them long before the SNP. Only recently, under Nicola Sturgeon's leadership, has the party unambiguously embraced social democracy. Under Alex Salmond, it refused to support a 50p tax rate and argued for a 3 per cent cut in corporation tax. If anything, as Stephen argued recently, it's the SNP that has been dragged leftwards by Miliband.

But in politics, perception matters more than reality. And as the most recent Scottish polls show (with the SNP reaching a new high of 54 per cent today), the perception that the nationalists are far to Labour's left is one that is doing them no harm at all.