Chapter 4: Decisions Under Risk

Question 1

Maximizing ____________ ____________ is NOT the same as Maximizing _____________ ______________ ______________.

Answer 1

Expected Value; Expected Monetary Value

Question 2

Three principles used for making Decisions Under Risk

Answer 2

Maximizing Expected Monetary Value (EMV)
Maximizing Expected Value (EV)
Maximizing Expected Utility

Question 3

Remember, Expected means…

Answer 3

Average

Question 4

Maximizing Expected Monetary Value (EMV)

Answer 4

Probability of the outcome (p) × monetary value of the outcome (m)

EMV = p₁ × m₁ + p₂ × m₂ + ….pₙ × mₙ

Question 5

Maximizing Expected Value (EV)

Answer 5

Probability of an outcome (p) × Value of an outcome (v)

EMV = p₁ × v₁ + p₂ × v₂ + ….pₙ × vₙ

Question 6

Utility of an outcome depends on how ____________ the outcome is from ____________ ____________’s point of view.

Answer 6

valuable; decision maker’s

Question 7

Principle of Maximizing Expected Utility
(The Expected Utility Principle)

Answer 7

Probability of an outcome (p) × Utility of an outcome (u)

EU = p₁ × u₁ + p₂ × u₂ + ….pₙ × uₙ

Question 8

Utils (see notes)

Answer 8

Utility derived from the square root of outcomes when calculating expected monetary value (EMV)

Question 9

Utils ONLY applies to ______________ ________________ _________________.

Answer 9

Expected Monetary Value (EMV)

Question 10

The Principle of Expected Utility measures more than _____________ ___________.

Answer 10

monetary utility

Question 11

We represent the utility of an oucome as ___(_______).

Answer 11

u(____)

e.g. utlity of 18 days at sea is u(18).

Question 12

2 Arguments for Expected Utility Principle

Answer 12

1) Principle of Large Numbers: In the long run, you’ll be better off if you maximize expected utility.

2) Axiomatic Approach: Derives Expected Utility Principle from fundamental set of axioms, regardless of what happens in the long run.

Question 13

Law of Large Numbers

Answer 13

After an ‘n’ number of trials approaches infinity, the difference between an expected and the average outcome, becomes arbitrarily small, tends to zero.

Question 14

Objection to Law of Large Numbers (Keynes)

Answer 14

“In the long run were all dead”

• Were never going to face an infinite number of decisions.
• In that vein, it doesn’t matter what the outcome (consequent) of my decision is.
  -whether I would be better off maximizing expected utility or infinite number of decisions is irrelevant, because I live a finite life.

(Law of Large Numbers shouldn’t be the basis for rational decision making under risk because it places us in impossible settings).

Question 15

Gambler’s Ruin

Answer 15

You and a friend each have a pot of $1000 total, made up several $1 bills.
Everytime a coin lands heads up, your friend pays you $1.
Everytime the coin lands tails up, you pay your friend $1.
As the game is played a SUFFICIENT amount of times, you and your friend will reach separate sequences of heads and tails.
Whoever reaches the end of this sequence first goes bankrupt. It’s IMPOSSIBLE to play forever, because either I’m gonna go bankrupt first or my friend is.
It would be better in the long run to maximize expected utitlity ONLY IF my pot is infinite, which is impossible.

Question 16

Axiomatic Approach

Answer 16

Principle of Expected Utility can be derived from axioms independent of what happens in the long run.

Question 17

The Axiomatic Approach tells us to maximize expected utility even if it’s a decision we only make ___________.

Answer 17

once.

Question 18

Two Types of Axiomatic Approaches

Answer 18

• Indirect Axiomatic Approach
• Direct Axiomatic Approach

Question 19

Indirect Axiomatic Approach

Answer 19

• Dominant Approach
• Decision maker doesn’t favor risky acts over other alternatives, even if the risky were of more utility.

-Decision maker makes a preferred set of alternatives they would rather do than risky act.
- If these set of alternatives follows constraints of axioms, then her decisions can be described AS IF she’s assigning numerical probabilities and utilities, and maximizing expected value.

Question 20

Direct Axiomatic Approach

Answer 20

Generates preferences over acts, from probabilities and utilities assigned to outcomes.

Question 21

The Utility of an _______ = the _____________ utility of it’s ______________.

Answer 21

Act; expected; outcome.

Question 22

Paradox

Answer 22

An argument against the expected utility principle.

Question 23

Sure-thing Principle

Answer 23

It doesn’t matter which alternative is chosen for states with the same outcomes

Decisions should be based on differneces between alternatives (outcomes).

Question 24

Allais Paradox (See Notes)

Question 25

Ellsberg Paradox (See Notes)

Question 26

Allais Paradox v. Ellsberg Paradox

Answer 26

Allais Paradox employed to avoid uncertainity in outcomes.

Ellsberg Paradox employed to avoid uncertainty in probabilities.

Question 27

St. Petersburg Paradox (See Notes)

Question 28

St. Petersburg Paradox (See Notes)

Question 29

Two-Envelope Paradox (See Notes)