Descriptive theories of rationality

Question 1

<p>Expected value theory</p>

Answer 1

<p>Your long-run “average”

What is to be expected if you choose an option an infinite number of times

EV = p(occurring) * (potential outcome) + p (not occurring) * (potential outcome)
</p>

Question 2

<p>Saint Petersburg Paradox</p>

Answer 2

<p>EV (game) = .5(2.00) + .25(4.00) +
.125(8.0) ….

= 1.00 + 1.00 + 1.00..
= INFINITE AMOUNT OF MONEY
</p>

Question 3

<p>

| Fechner&rsquo;s Law</p>

Answer 3

<p>
	Psychological intensity is a logarithmic f(n) of physical intensity Just noticeable differences</p>
<p>
	 </p>
<p>
	 </p>

Question 4

Utility Curve implies _____ ______

Answer 4

risk aversion

Question 5

Concave Utility function: Gamble 1: What do you prefer
A: $100
B. .5 ($200)
.5 (0)
Concave utility function explains ____ _______

Answer 5

A: $100

Risk aversion

Question 6

Expected Utility Theory is a _________ theory of behavior that does not explain ____?______; but how people….

Answer 6

Normative theory of behavior

Does not explain how people behave

how they SHOULD behave if they followed certain requirements of rational decision making

Question 7

What are the six principles of the expected utility theory?

Answer 7

principle 1: Ordering 
principle 2: Dominance 
Principle 3: Cancellation 
principle 4: Transitivity (EU Axiom)
principle 5: Independence 
Principle 6: Invariance (distribution of probabilities across alternatives)

Question 8

Principle 1 of the EU:

Ordering

Answer 8

Principle 1: Ordering

Rational decision-makers should be able to compare alternatives

comparability Axiom of EU

Question 9

Principle 2 of the EU:

Dominance

Answer 9

Principle 2: Dominance

Car A is $ 15,000 and gets 35 MPG
Car B is $20,000 and gets 28 MPG

A = much better (it dominates) B

Question 10

Principle 3 of the EU:

Cancellation

Answer 10

Principle 3: Cancellation

Decisions are made by comparing differences.

Similarities cancel out

Independence Axiom (EU)

Question 11

Principle 4 of the EU:

Transitivity (EU Axiom)

Answer 11

Principle 4: Transitivity (EU Axiom)

If A > B and B > C, then A > C

Question 12

Principle 5 of the EU:

Independence

Answer 12

Principle 5: Independence

The preference between two option must not be affected by a third outcome that is equal to both options)

pertains to well-defined preferences and assumes that two gambles mixed with a third one maintain the same preference order as when the two are presented independently of the third one

Question 13

Principle 6 of the EU:

Invariance (Distribution of probabilities across alternatives)

Answer 13

Principle 6: Invariance (Distribution of probabilities across alternatives)

A decision maker should not be affected by the way that the alternatives are presented

Ex) Choose between:
A two-stage lottery that pays out $100 if you win both stages (p= .50 to win at each stage), OR
25% chance to win $100 in a once-and-done lottery

Question 14

Define: Axiom

Answer 14

a statement or proposition that is regarded as being established, accepted, or self-evidently true.

Question 15

Expected Utility Theory Axioms:

EU established explicit axioms that underlie _______ _______ _______

When axioms are satisfied, a ________ ________ can be associated with each consequence.

Answer 15

Rational decision-making

Numerical measurement

Question 16

Name three examples of Paradoxes in Rationality:
1)
2)
3)

Answer 16

1) Loss Aversion
2) Allais Paradox
3) Ellsberg Paradox

Question 17

Paradoxes in Rationality: Loss Aversion

Answer 17

Gamble 1: flip a coin: head: $10; tail: $0 vs. $5 for sure

Gamble 2: flip a coin: head: -$10; tail: $0 vs. -$5 for sure

Gamble 3: you are given $10, then play Gamble 2, people flip a coin

Question 18

Paradoxes in Rationality: Allais Paradox

Answer 18

Demonstrates the Independence Axiom

Question 19

Paradoxes in Rationality: Ellsberg Paradox

Answer 19

It is generally taken to be evidence for ambiguity aversion