HW XXXXXXXXXXInformation Aggregation XXXXXXXXXXThe purpose of this question is to review some of the probability theory that is relevant for information aggregation. A coin is weighted so that it...

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HW 6 (+15) Information Aggregation 1. (+4) The purpose of this question is to review some of the probability theory that is relevant for information aggregation. A coin is weighted so that it lands on “heads” 75% of the time. The coin is flipped twice, with the same outcome each time. Given that the outcome is the same on both flips, how likely is it that the outcome was “heads” both times, not “tails” both times? 2. (+8) Ann, Bonnie, and Cindy must together choose between alternative ?? and alternative ??, which are equally likely to be superior. Individually, each has probability ?? = .7 of determining which alternative is truly superior, and their three opinions are statistically independent. a. (+4) What is the probability with which two or more of them correctly identify the superior alternative? b. (+4) Now assume that Cindy is biased, and votes for ?? regardless of which alternative she believes is superior. How likely is ?? to win when ?? is superior? How likely is ?? to win when ?? is superior? Given that these two cases are equally likely, what is the overall probability of a correct decision? 3. (+3) How would you classify the following political issues: largely common interest or largely private interest? Explain your answer. a. (+1) The question of whether to increase Provo taxes to raise money to rebuild Timpview High School. b. (+1) The question of whether to allow or prohibit abortions. c. (+1) The question of whether to require masks in public spaces or not, during a pandemic. HW 6 (+15) Information Aggregation