HW XXXXXXXXXXPreference Aggregation XXXXXXXXXXTo illustrate the Rae-Taylor theorem, consider an electorate consisting of Alexandria, Beverly, and Cindy. Preferences are statistically independent, and...

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HW 5 (+18) Preference Aggregation 1. (+10) To illustrate the Rae-Taylor theorem, consider an electorate consisting of Alexandria, Beverly, and Cindy. Preferences are statistically independent, and each is equally likely to support (S) or oppose (O) a future bill, which may pass (P) or fail (F). a. (+6) Rae and Taylor assume that gains and losses are symmetric, so that utility is simply ??(??|??) = ??(??|??) = 1 and ??(??|??) = ??(??|??) = −1. In this case, What is Alexandria’s expected utility, under unanimity rule (i.e. the bill fails unless everyone supports it) and under majority rule (i.e. the bill fails unless two voters support it)? Which system does Alexandria prefer? b. (+4) Now suppose that voters really dislike passing a bill that they oppose, so that ??(??|??) = −5 (other utilities remain unchanged). Now what is Alexandria’s expected utility, under unanimity rule and under majority rule? Which system does Alexandria prefer? 2. One silly way to make collective decisions would be to say that policy ?? will be implemented unless everyone favors ??, in which case policy ?? will be implemented instead. Explain how this Silly Rule does or does not satisfy each of May’s axioms, listed below: a. (+2) Decisiveness b. (+2) Anonymity c. (+2) Neutrality d. (+2) Monotonicity HW 5 (+18) Preference Aggregation