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Some did, some didn't, some abstained because they thought both the Tory and labour ideas were shit.
Labour's counter motion was some weak-ass-shit and did nothing to address the bigger issues in the private rented sector.
Paying the same to house one person in a three bed house as five people in a one bed flat doesnt make sense and needed addressing, it was done badly, obvs, but even a fifth of labour MPs abstained rather than voting against including Diane Abbott, Chuka Umunna and Gordon Brown. Maybe even Ed Balls.
Again, I suspect by the fact you're using the term bedroom tax you're just reading the headlines and labour leaflets. Have a read of Andrew George's affordable homes bill. That's what the lib dems wanted and it's good.
Coalitions demand unfortunate compromise and it makes me sad to think about them too.
I'm a bit of lib dem sympathiser as my local lib dem mp is a decent, principled fellow who has regularly voted against his party when they've got it wrong, like on tuition fees.
They're easy to hate at the moment, but only if you just believe what's written in the right-wing press and labour promotional material. If you use google instead you find stuff like this :
http://www.markpack.org.uk/129190/what-the-lib-dems-have-stopped-the-tories-doing/