Preferences and choice

Question 1

What are the 3 axioms within preferences?

Answer 1

1) Reflexivity
2) Completeness
3) Transitivity

Question 2

What does it mean if all 3 of the preference axioms are true?

Answer 2

Preferences are ordering

Question 3

What does reflexivity mean?

Answer 3

For all x ε X, we have xRx

Question 4

What does completeness mean?

Answer 4

For all x,y ε X, either xRy or yRx, this rules out not being able to compare 2 alternatives

Question 5

What is transitivity?

Answer 5

For all x,y,z ε X, if xRy and yRz then xRz

Question 6

What is a choice function?

Answer 6

Given what is available, the choice function tells us a subject of this

Question 7

What makes a choice function rationalizable?

Answer 7

C is rationalizable if there exists R such that C(s) = M(R, S)

If a preference relation is ruling C, then given what is available C tells us the set of “best” alternatives for him

Question 8

Explain property α

Answer 8

Suppose two sets of alternatives such that one is included in the other. Whatever I chose from the smaller set includes whatever I choose from the bigger set that is available in the smaller set.

Question 9

What is property β

Answer 9

Can’t go from indifferent to not preferred as the set gets larger.

Question 10

What is the weak axiom of revealed preference (WARP)?

Answer 10

If given a set, I choose one thing over another, if I choose the other, it must be because the first alternative is not available.

Question 11

What is a social choice rule?

Answer 11

A social choice rule (aggregation rule) is given by F: {Ri} iεN -> R, where R is a preference relation (for the group of individuals) which we assume to be complete and reflective on X.

Question 12

What is an unrestricted domain?

Answer 12

f can deal with any possible individual preferences.

Question 13

What is the Pareto principle?

Answer 13

If xPiy for all iεN then xPy

Question 14

What is the axiom: independence of irrelevant alternatives (IIA)?

Answer 14

For any two R, R’ and any two x,y ε X if R and R’ rank x relative to y the same then so does R and R’.

If given 2 sets of preferences for everybody, if all rank one alternative the same relative to another, then the aggregate preferences given the 2 sets of preferences also ranks theses two alternatives the same.

Question 15

What is Arrow’s impossibility theorem?

Answer 15

The only social choice rule that satisfies unrestricted domain, Transitivity, pareto principle and Independence of irrelevant alternatives (IIA) is the dictatorial one

Question 16

What is a dictatorial choice function?

Answer 16

There exists i ε N such that R (groups preference) equals Ri (dictators preference) for some i.

The preferences of the group are those of one individual (the dictator)Wh