Lecture 4

Question 1

Value

Answer 1

Objective, monetary value of something. Only applies to options that are certain, not gambles (in which case you use EV)

Question 2

Expected Value

Answer 2

EV = p(outcome 1)v(outcome 1)+p(outcome 2)v(outcome 2)…

Difference between EV and value is that EV takes into account both the monetary value and probability of something. Useful for seeing the value of a gamble.

Question 3

Utility

Answer 3

The subjective value of something, measured in utils (an arbitrary measure for comparing subjective value across people). Only used for options that are certain, not gambles (in which case you use expected utility)

Question 4

Expected utility

Answer 4

Unlike utility, takes into account both subjective value (utils) and likelihood - multiply outcome probabilities by utils. Useful for seeing value of gamble.

Question 5

Subjective expected utility

Answer 5

Unlike expected utility, takes into account subjective likelihood of each outcome along with subjective value. This happens because people have different ideas of how likely things are in the real world. Often more applicable to decisions other than coin tosses because sometimes the probability of something occurring just isn’t certain. Other times, the probability may be known but we may under or over-weigh it.

Question 6

Expected Value Theory

Answer 6

Uses EV to predict behavior: people should choose option with highest EV. Problems: how to deal with St. Petersberg Paradox and non-monetary gambles?

Question 7

St. Petersberg Paradox

Answer 7

Toss coin as many times as needed to score a head. You get 2^n dollars for playing, so if H on toss 1, $2; toss 2, $4; etc. How much should you pay to play? Using EV, the numbers cancel out and you get infinity. But nobody would pay that amount (though normative) to play. Why? Diminishing marginal utility. Does this violate Expected Value Theory though?

Question 8

Diminishing marginal utility

Answer 8

Each additional unit of wealth worth less than the one before, so at some point getting richer does not improve your happiness.

Question 9

Expected Utility Theory

Answer 9

Created to deal with problems of Expected Value Theory. Axioms that underlie rational decision making: connectedness (ordering of alternatives), dominance, transitivity, independence (cancellation principle). If these outcomes are violated, then expected utility is not maximized.

Question 10

Connectedness (ordering of alternatives)

Answer 10

Expected Utility Theory. Given 2 alternatives, rational decision makers should be able to compare and prefer one or be indifferent. Ability to rank alternatives - no refusal to choose.

Question 11

Dominance

Answer 11

Expected Utility Theory. Rational decision makers should always pick the dominant alternative. Weak dominance: better on at least one dimension, and equal on all other dimensions. Strong dominance: better on all dimensions. Therefore, pick the best choice.

Question 12

Transitivity

Answer 12

Expected Utility Theory. If you prefer a>b and b>c, then you must prefer a>c

Question 13

Independence (cancellation or sure-thing principle)

Answer 13

If two alternatives have identical and equally probable outcomes among all probable outcomes, then the utility of those outcomes should cancel out and not figure into ultimate choice.

Question 14

Violations of connectedness/ordering of alternatives

Answer 14

Sophie’s Choice - a choice you can’t make. Some outcomes where it is uncomfortable or unethical to make a tradeoff.

Question 15

Violations of transitivity

Answer 15

If there are two considerations or rules underlying ordering of choice, violations of transitivity may occur.

Question 16

Violations of independence

Answer 16

Allais Paradox - most people fail to cancel out and make the same choice.

Question 17

Do violations of Expected Utility Theory mean that decision makers are irrational?

Answer 17

Not always - people use heuristics to save energy and time. There are pros and cons to these.