The Theory of
Rational Choice
The Theory of Rational Choice
A rational decision-maker chooses the best
action according to her preferences, among
the actions available to her.
•Set of available actions
•Preferences
–Complete
–Consistent (transitive)
Rational  Selfish
The Theory of Rational Choice
Payoff function: associates a number with
each action in such a way that actions with
the higher number are preferred.
a and b

A
u(a) > u(b) if and only if the decision-maker
prefers a to b
The Theory of Rational Choice
Example:
A = {Coke, Pepsi, Sprite} = {C, P, S}
Decision-maker prefers C to P and P to S
1. u(C)=3, u(P)=2, u(S)=1
Or
2. u(C)=10, u(P)=0, u(S)=-2
The Theory of Rational Choice
Preferences  Ordinal information
v is another payoff function that represents
the same preferences as u if
v(c) > v(p) u(c) > u(p)
Any monotonically increasing function of u
represents the same preferences
The Theory of Rational Choice
Example:
u(C)=3, u(P)=2, u(S)=1
u(C)=3 > u(P)=2 > u(S)=1
f(x)=2*x
v(x) = f(u(x))
v(C) = f(u(C)) = f(3)=6, v(P)=4, v(S)=2
v(C)=6 > v(P)=4 > v(S)=2
The Theory of Rational Choice
The action chosen by a decision-maker is at least as
good, according to her preferences, as every other
available action.
Example:
If A={P,C} and she always chooses C
If A’={P,C,S} and she chooses P
Inconsistent with the Theory of Rational Choice
To be consistent she must choose C or S
- See the Weak Axiom of Revealed Preference
(WARP)