I have not heard of Chesterton’s Fence.
I do know who G.K. Chesterton is but am not aware of his views on the electoral college or whether you refer to some other Chesterton, a person and place, and how this fence, physical, metaphorical, or legal, relates to the electoral college.
Since I and others do not want to be as uninformed as Mr. Holder, the hero of Ruby Ridge and Waco, please share the information needed to resolve the question posed by your statement (and its assumption that this is commonly known information...)
The quotation you’re looking for is from Chesterton’s 1929 book, The Thing, in the chapter entitled, “The Drift from Domesticity”:
In the matter of reforming things, as distinct from deforming them, there is one plain and simple principle; a principle which will probably be called a paradox. There exists in such a case a certain institution or law; let us say, for the sake of simplicity, a fence or gate erected across a road. The more modern type of reformer goes gaily up to it and says, “I don’t see the use of this; let us clear it away.” To which the more intelligent type of reformer will do well to answer: “If you don’t see the use of it, I certainly won’t let you clear it away. Go away and think. Then, when you can come back and tell me that you do see the use of it, I may allow you to destroy it.