Not to be dismissive, but this is a pretty unhelpful approach to the voting problem. The idea of picking a random person is motivated by the thought that the mo

Not to be dismissive, but this is a pretty unhelpful approach to the voting problem. The idea of picking a random person is motivated by the thought that the more support a candidate has the greater chance they have of being selected. But then why not just select the person with the highest probability of being selected? The difficulty is that even this "harmless" process is infected. The real upshot of Arrow's theorem is that you can't aggregate preferences: there is no "measure theory" underlying the concept of group will.