University of Delhi 2011 M.A Economics winter semester 108- social choice theory (admissions of 1999 & onwards) - Question Paper

[This question paper contains 3 printed pages.]

Your Roll No.

M.A. Winter Semester

ECONOMICS - Course 108 *

Social Choice Theory

(Admissions of 1999 and onwards)

Maximum Marks : 70

(Write your Roll No. on the top immediately on receipt of this question paper.)

Answer any four questions.

1. (a) Suppose R stands for a weak preference relation defined over X. Let R be complete. Then examine the validity of the following statement: For all x, y, z e X, [xly & yPz xPz] - [xRy & yRz > xRz] where P and I respectively stand for strict preference relation and indifference relation.    (5*/2)

(b) Show that WARP <-> ACC if the choice function has unrestricted domain. How does the result change if domain is restricted ? Also show that with restricted domain, Arrow consistency Condition does not rule out irrational choice,, functions.    (6+3+3)

2.    (a) Consider the following choice function defined over

X - {x, y, z) : C({x!|y}) - {x}, C({y, z}) = {y, z}, C({x,z}) - {/}, Cr({x, y, z}) = {z}. Does this choice function satisfy Path Independence ? Is this choice function rational ? Also, check if it satisfies quasitransj'tive rationality and transitive rationality.    (2+3+4)

(b) Show that Path Independence a & .

(8fc)

ii

3.    (a) Construct a colledtive choice rule satisfying

monotonicity but violating strong monotonicity.

(6)

(b)    Construct a Social Welfare Function satisfying unrestricted domain, weak Pareto and Non-Dictatorship.    (6)

(c)    Construct a Social Welfare Function satisfying

unrestricted domain, weak Pareto and Non-

Dictatorship.    j    (5/2)

11

4.    (a) Suppose number of alternatives is greater than

number of individuals. Show that any Social Decision Function satisfying Neutrality, Monotonicity and Independence will give some one veto power. What happens if the assumption on number of alternatives is violated ?    (9)

(b) Show that any decisive collective choice rule satisfying Neutrality, Independence, Strict Monotonicity and Anonymity must be the simple majority rule.    -    (S'/i)

5. (a) Let C be a choice function defined over X satisfying properties a & p. Let R_c be defined as : For all x, y e X, xR_cy iff x e C({x, y}). Then show that for all x, y, z e X, xP_cy & yP_cz xP_cz.    (SA)

(b) Develop a framework of Rights and define Sens minimal libertarianism condition. Prove the theorem known as Liberal Paradox. Why does Sen think that modification of weak Pareto principle is necessary to solve this impossibility ?

(3+5+4)

(200)****

Attachment: university-of-delhi-2011-m-a-economics-35492-1.pdf

Earning:   Approval pending.