HW XXXXXXXXXXPreference Aggregation
XXXXXXXXXXTo 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?
. (+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
. (+2) Anonymity
c. (+2) Neutrality
d. (+2) Monotonicity
HW XXXXXXXXXXPreference Aggregation