6: Social Choice: Spacial Models

Question 1

When considering single peaked preferences, what can be said about the middle option

Footnote
1D policy space

Answer 1

It can not be worst of three

Question 2

Blacks Median voter theorem

Footnote
1D policy space

Answer 2

If all voters have single peaked preferences, the ideal point of the median voter is a condorcet winner

Question 3

Blacks single peakedness theorem

Footnote
1D policy space

Answer 3

if all voters have single peaked preferences, pairwise majority voting gives rational preferences

Question 4

What can be said for three voters majority voting in two dimensions?

Answer 4

For any point, there exists another point prefered by at least 2 voters

Question 6

Theorem by McKalvey

Footnote
SPP in min 2D

Answer 6

a condorcet winner exists only for very certain ideal points

Question 7

Consequence of the theorem by McKalvey

Footnote
SSP in min 2D

Answer 7

Movement from any point to any other point is possible by a sequence of pairwise majority votes

Question 8

How do I use the Lagrange-Method for maximizig f(x) under the constraint g(x)

Answer 8

g(x) is the constraint solved for 0

L= f(x)+\lambda*g(x)

L nach x und \lambda ableiten

Gleichungssytem lösen (erst nach \lambda)