It is not the first time that Mr. Cain has floated the idea of an electrified fence. He has told the story many times of a caller to his former radio show who chastised him for talking about building a border fence, saying that such an idea was impractical. Mr. Cain often says he told the caller that he had recently returned from China, and if the Chinese could build the Great Wall then America could build a border fence.

Last summer, after President Obama remarked that some Republicans seemed to want a moat filled with alligators in addition to a fence, Mr. Cain responded by saying that he would indeed add an alligator-filled moat to his proposed fence, which would be topped with electrified barbed wire.

In his remarks on Saturday, Mr. Cain appeared to go a step further. Speaking to a rally sponsored by the Roane County Tea Party, Mr. Cain said that part of his plan would be to “secure the border for real” with a fence.

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