15/10/2012 10:48 BST | Updated 15/12/2012 05:12 GMT

Who Benefits From a Lib Dem Collapse?

The Liberal Democrats have now been flatlining at or just below 10% of the vote for nearly two years. The decision to join the Conservatives in a coalition government looks more electorally toxic with each passing month. It is thus no surprise that bloggers and strategists for both major parties have begun to speculate about the implications of a Lib Dem collapse for their parties.

Some have argued that the Conservatives stand to gain disproportionately, owing to the large number of seats in the South East and South West where the Lib Dems compete with the Tories, with Labour a distant third. If Lib Dem votes in the South East and South West head over to Labour, the Tories are the big winners, or so the reasoning goes.

This argument is misleading - such arguments focus on where the Lib Dems are most competitive and ignores the fact that they win large numbers of votes in places where they are not electorally competitive at all. For example, there are around 50 marginal seats with Tory MPs and Labour challengers where the third place Lib Dem vote is more than twice the margin of victory. If the Lib Dem vote heads red in these seats, Labour are big beneficiaries. And there are other combinations, such as Lib Dem seats where Labour are the main challengers.

A more systematic way to look at the issue is to imagine what happens in every seat if we reallocate some of the Liberal Democrats' votes. Nick Clegg's party have made this job easier by vowing to vote against the expected changes to parliamentary boundaries, so we can simply use the 2010 constituency boundaries. We can therefore apply shifts in the Liberal Democrat support at constituency level to get a rough idea about their likely effects on the balance of power

Where have the Lib Dems gone? Mark Pack's excellent analysis of "lost Lib Dem" voters from autumn 2011 found that 75% of 2010 Lib Dem voters were no longer supporting the party a year later - 26% had gone over to Labour, 24% to "don't know", 9% to the Conservatives and 15% to other options. Looking in depth at the "don't knows", we find this is a group that is closer to the left than the right - one measures such as views of the parties and left-right ideology, they look more like Lib Dem defectors to Labour than Lib Dem loyalists or Lib Dems who have defected to the Conservatives. However, many of them are clearly reluctant to make the shift over to Labour, despite the coalition, so clearly retain some loyalties to their former party. I therefore split them 50-50 between the Lib Dems and Labour. For simplicity, I allocate the "other" vote to the Greens, who as the largest left wing minor party are the likeliest destination for disaffected Lib Dems.

The Lib Dems won 23.6% of the Great British vote in 2010 (Northern Ireland is excluded as none of the major parties contest it). Reallocating their votes in accordance with Mark Pack's poll results, and leaving everything else unchanged in the following national vote shares for each party:

Labour: 38.7% ( +9.0)

Conservative: 39.1 (+2.1)

Lib Dem: 9.0 (-14.6)

Green: 4.5 (+3.5)

The current pattern of Lib Dem vote shifting would thus point to a near tie in the popular vote, all else being equal. But how would this translate into seats? Wouldn't the Conservatives get an advantage from all the Liberal Democat-Conservative marginals in South England. There are two ways we can test this. The first is to apply a "uniform swing" adjustment to the vote shares in each constituency - reallocating the parties' vote share in accordance with the national shift in their vote. Doing this results in the following allocation of seats:

Seat allocation - Uniform swing in each constituency

Labour 320 (+62)

Conservatives 294 (-13)

Lib Dems 11 (-46)

Others: 25

Hung Parliament: Labour six seats short of a majority

Clearly, the Conservatives are not the big winners from a Lib Dem collapse in this model. They do pick up more former Lib Dem seats than Labour do (28 to 18) but this is more than offset by the large gain Labour makes in marginal seats where they are challenging the Conservatives and the Lib Dems are third. A collapse in Lib Dem vote in these seats hands them an extra 41 seats, enough to get them very close to a majority. An alliance with the surviving 11 Lib Dems would put them over the top with a 12 seat majority.

This seat allocation suggests that Labour's often overlooked advantage from the electoral system would remain significant even if the Lib Dems' support shrunk dramatically. The UNS method relies on some rather unrealistic assumptions, however. We are reallocating 15 percentage points of Lib Dem support in each seat, but in many seats this amounts to the entire Lib Dem vote, or even more than the total Lib Dem support base. While vote swings in Britain tend to be quite uniform, it isn't that plausible to imagine that the entire Lib Dem support base will switch away (and certainly implausible to imagine that more voters will switch than voted Lib Dem in the first place!)

A different way of attacking the problem is to propose a proportional swing of Lib Dem supporters. Rather than deducing 15 percentage points from the Lib Dem total in each seat, and reallocating it, we split the Lib Dem in accordance with the ratio's found in Mark Pack's survey. What happens then? It is not as straightforward to calculate national vote shares using this method, so I focus on the shift in seat allocations.

Seat allocation - proportional swing in each constituency

Labour 312 (+54)

Conservatives 309 (+2)

Liberal Democrats 0 (-57)

Others: 29

Hung Parliament, Labour 14 seats short of a majority

Allocating the Liberal Democrats' vote proportionally completely wipes them out at Westminster, as there are no Lib Dem seats so secure that the party can hold on with only 37% of its 2010 vote. This is an extreme, though not impossible, outcome: in 2011 the Liberal Democrats lost all nine of their constituency seats in Scotland, clinging on in Parliament only through proportional top up seats and votes from the Shetland and Orkney Isles. While a wipeout on this scale is fairly unlikely, it does provide a neat test of the relative effect of Lib Dem seat changes, as in this case all Lib Dem seats are awarded to someone else. The Conservatives do perform better in this situation, winning 33 Lib Dem seats to Labour's 23 (and 1 for the SNP), but this is once again offset by Labour gains in Con-Lab marginals, where Ed Miliband's party pick up 30 seats. Once again, Labour are the major winners from a Lib Dem collapse, although they would be faced with a very difficult hung parliament.

We can see from both scenarios that Labour are most likely to gain from a collapse in Lib Dem support, as any gains the Conservatives make at the Lib Dems' expense are more than offset by the boost Labour gets in Con-Lab marginal seats. This is evidently not a realistic exercise, ignoring factors such as incumbency effects, local campaigns and tactical voting. However, all these factors are likely to further advantage Labour. If Liberal Democrat incumbents are able to shore up their support, this will hurt the Conservatives more than Labour as the Tories are the second place party in most Lib Dem held seats (38 vs 17 with Labour second). Lib Dem local campaigning will also be more likely to benefit them in seats they hold or have a chance of winning than in Con-Lab marginals where the Lib Dems are out of contention. It still seems plausible that many left-leaning voters will ultimately tactically support the Liberal Democrats to keep out Conservative challengers at local level when Labour have no chance, while at present it is open to doubt whether Conservatives, who regard their junior partner with growing hostility, will be willing to lend their votes to Lib Dem challengers.

The collapse in the Lib Dem vote is therefore most likely to benefit the Labour party and make a Parliamentary majority for Cameron's Conservatives even more of a stretch, though Lib Dem defections alone would probably not deliver Labour a majority. It would seem, therefore, that the Conservatives have a strong interest in helping to restore the fortunes of their junior Coalition partner. Yet recent Conservative party behaviour - in particular the 'white van man' approach shown at their recent conference, with authoritarian attacks on welfare recipients, the EU and crime, while slapping down Lib Dem proposals such as the 'Mansion Tax' - seems almost designed to antagonise the Lib Dems and encourage further bleeding of support. This is a dangerous strategy. Even if David Cameron manages to consolidate his right flank, he is likely to lose the next election if his junior Coalition partner collapses and the centre-left vote consolidates behind Ed Miliband's Labour.