The British fallacy as it is called sometimes, is the argument that the middle-ground between two debaters is most likely the accurate one.
I say there is no God, you say there is a God, so lets say there could possibly be a god. This is a fallacy in most cases, due to the fact that it argues a middle-ground without regard for the positions. The absurdity becomes clear when you put it in a mathematical perspective:
Person 1: 2 + 2 = 4
Person 2: 2 + 2 = 6
Conclusion: 2 + 2 = 5
I don’t have much to say on this fallacy, but it does tend to pop up where you have 1 party who has taken an extreme position vs a moderate opponent, who then tries to use the fallacy to “trick” their opponent over to their side.
You can see this in both American and European politics in different perspectives. Where in the US the “Left – Right” center line has been drawn very much in “moderate-right” and in Europe where the center line has been drawn in the “moderate left” perspective.