the other with top on 0 (orderings {ж} >~4 B >-4 D, B >b D >-δ {ж}, and
B {x} D).
Proof of Theorem 1 To prove necessity, let F∙. An —> 2κ be a strategy-
proof social choice function and let {Bi,..., Bq} be the minimal Cylindric
decomposition of ⅛, which exists by Proposition 3.
(1) Assume that x,y ∈ Zi ∈ AC(Bp) = {Z1,Z2}. Since {Bi,..., Bq} is
minimal we have that Zi ∩ Z2 = 0. Assume that W''' ≠ TV™; that is, there
exists I ∈ W''' such that I TV™. Consider any P such that τ(Pi)Γ∖Bp = Z1
for all i ∈ I and τ(Pf) ∩ Bp = Z2 for all j ∈ N∖I. Then, x ∈ F(P) and
у <f F(P) contradicting that x and у belong to the same active component
of Bp.
(2) Assume x ∈ A, у ∈ Y, and AC(Bp) = {A, У}. To obtain a contra-
diction assume there exists D ∈ W''' and N∖D ∈ TV™. It is easy to find P
such that x, у ∈ F(P) contradicting that x and у belong to different active
components of Bp.
(3) Follows from part (a) of Proposition 4 and Proposition 5.
Sufficiency follows from part (b) of Proposition 4, since it is clear that
all social choice functions defined on each of the sections are onto the active
components of the section and strategy-proof.
6 References
ANSWAL, N., CHATTERJI, S., and SEN, A. (1999). “Dictatorial Do-
mains”, Discussion paper 99-05, Indian Statistical Institute.
BARBERÀ, S., GUL, F., and STACCHETTI, E. (1993). “Generalized Me-
dian Voter Schemes and Committees”, Journal of Economic Theory, 61,
262-289.
28
More intriguing information
1. The name is absent2. The name is absent
3. Rent Dissipation in Chartered Recreational Fishing: Inside the Black Box
4. Inflation Targeting and Nonlinear Policy Rules: The Case of Asymmetric Preferences (new title: The Fed's monetary policy rule and U.S. inflation: The case of asymmetric preferences)
5. Sex-gender-sexuality: how sex, gender, and sexuality constellations are constituted in secondary schools
6. A Unified Model For Developmental Robotics
7. The name is absent
8. Orientation discrimination in WS 2
9. Globalization, Divergence and Stagnation
10. The name is absent