Chapter 2: Preference and Choice
• Two approaches to modeling individual choice behavior:
1. Preference-based approach: preference relation
2. Choice-based approach: revealed preference
• A set ( X ) of possible (mutually exclusive) alternatives from which the individual
must choose.
2. A: Preference Relations
• Preference relations ≿, which is a binary relation on the set of alternatives X
We read x ≿ y as “x is at least as good as y”, where x,.y ∈ X
1. x ≿ y but not y ≾ x ⇔ x f y
2. x ≿ y and y ≾ x ⇔ x ~ y
• Definition : The preference relation ≿ is rational, if it satisfies:
Axiom 1: Completeness. For all x, y ∈ X , we have that x ≿ y or y ≾ x or both.
Axiom 2: Transitivity. For all x, y, z ∈ X , if x ≿ y and y ≿ z, then x ≿ z.
⇒ The individual pletely rank any elements in X.
However: Do we really know our own preferences?
Are our preferences really transitive?
Just perceptible differences, the framing problem, collective decision
(Condorcet paradox)
1
2. B: Choice Rules
• A choice structure (B, C(•)), where B is a family of nonempty subsets of X, C(•) is a
choice rule.
• The weak axiom of revealed preference: if for some B∈B with x,y ∈ B we have
x ∈ C(B) , then for any B'∈B with x, y ∈ B' and y ∈ C(B' ) , we must also have
x ∈ C(B') .
Example: X = {}x, y, z , and B = {{x, y
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