In the game "20 questions", one player (the "leader") thinks of a concept, and the other players ask 20 yes-or-no questions in attempts to guess that concept. In this game, the players extract 20 bits of data from the leader, which (if the questions are selected wisely) is enough data to single out one concept from a set of roughly one million concepts (1048576, to be precise).
Three bits of data are required to specify one of the hands of one of your biological grandparents: One bit for "maternal" or "paternal", one bit for "male" or "female," one bit for "left" or "right."
The president of the United States of America is selected from a set of about 320,000,000 people. This selection encodes roughly 28 bits of data. Where do those bits come from? Between 1/4 and 1/2 of the population is eligible for the presidency, so 1-2 bits come from constraints on who is allowed to be president. Another ~1 bit comes from the voters in the presidential election (when one candidate is selected from a set of two finalists). 2-4 more bits come from the primary elections (when the two finalists are selected from a set of ~4-32). However, most of the bits that go into choosing the president — 21 or more of them — come from self-selection and private politicking.