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In the 2010 UK general election, the Conservatives won 307 seats, Labour won 258 and the Liberal Democrats won 57, with the rest won by various minor parties. Now, the Lib Dems could have conceivably helped keep the Labour Party in government, but not alone: together they would make a total of 315 seats, when 326 would be needed for a majority (or 323 if you discount the seats won by Sinn Fein). So a returned Labour government would've also needed the support of other minor parties: the SDLP (3 seats) and the Alliance Party (1 seat) would be most likely to go along given their affiliations with Labour and the Lib Dems respectively; they'd also need some combination of the SNP (6 seats), Plaid Cymru (3 seats) and the Green Party (1 seat). It could've been done, but it would've been really unwieldy.

So, the question is: what if the Lib Dems had won enough seats that they could've conceivably made up a majority with either the Conservatives or Labour just by themselves, without those other minor parties needing to be involved? Would they have been any likelier to form a coalition with Labour, or possibly to switch from one party to the other mid-term?


(By the way: I checked out the 2010 results and out of the 13 seats the Lib Dems lost in that election, six of them were lost by tiny margins – five to the Conservatives, one to Labour. That's still not enough to make it to 326 or even 323, so let's say Labour kept a few extra seats from going Conservative as well.)
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