This is basically the central theme of one of Asimov's short stories. In the story a giant computer called the multivac selects one person that it deems statist

This is basically the central theme of one of Asimov's short stories. In the story a giant computer called the multivac selects one person that it deems statistically representative of the entire nation, asks them a couple of questions then uses their answers to "elect" the next president.