Most mice will rush this one. Since they begin split between both sides, the platform usually remains relatively balanced... at first.
Go for the cheese only if you notice that more mice are going for it on the other side than there are on your side. Otherwise, you might end up tipping the platform over.
The shaman usually has two options: either get to the middle as soon as possible and stabilize the platform with an anchored plank, or wait until the platform falls and build a bridge across. Choose the former if you want to try and save more mice; the latter if you don't want to take risks.