HW XXXXXXXXXXChaos Theorem
XXXXXXXXXXFive voters have single-peaked preferences (with circular
indifference curves) over a two-dimensional policy space, with ideal points
(−2,0), (0,−2), (0,0), (2,0), and (0,2).
a. (+6) Show that the policy (0,0) is a Condorcet winner (that is, that is is
majority prefe
ed to any policy in the two-dimensional space, not just
to the five ideal policies).
. (+6) The status quo is (−1,0), but an agenda setter with ideal point
(0,2) (who has no voting power) proposes a single new policy pair,
which is adopted if prefe
ed by a majority. What should she
propose? (Assume indifferent voters accept the proposal.) What if the
status quo is (0,0)?
c XXXXXXXXXXIn class, we demonstrated that, when no Condorcet winner
exists, an agenda setter can pit sincere voters against one another to
eventually get her ideal policy. How does this change when a
Condorcet winner exists?
HW XXXXXXXXXXChaos Theorem