Henry Farrell ponders the British debate:

If the debate has significant long term consequences for public opinion, as Rachman argues (perhaps from hope as much as rigorous analysis) then this would diverge from the findings of US political scientists, who argue that the effects of presidential debates on public opinion are moderate at best. Such divergence might be a bit embarrassing for me - I made a strong version of the they don’t matter’ argument to a bunch of politically interested Brits at dinner a couple of weeks ago. But it would be intellectually pretty interesting.

He goes on to speculate that America's strong two party system may make debates less important.
