Chapter 3: Decisions Under Ignorance

Question 1

Ignorance

Answer 1

Decision maker

1) knows outcome and what outcome may result in.
2) can’t assign a probability states corresponding to outcomes.

Question 2

The _____________ principle states that ______________ acts (where one act is clearly worse than another) must ____ be chosen.

Answer 2

Dominance; dominated; NOT

Question 3

aᵢ ≻ aⱼ

Answer 3

Act “i” is better than Act “j”

This means one is rationally required / ought to choose act i

Question 4

aᵢ ⪰ aⱼ

Answer 4

Act i is at least as good as Act j

Question 5

aᵢ ~ aⱼ

Answer 5

Act i and Act j are equally rational.

Question 6

v(a₁, s₁) = 1

Answer 6

The value of doing act 1 in state 1 equals, should state 1 be the true state of the world, is 1 (ordinal ranking).

Question 7

Weak Dominance

Answer 7

aᵢ ⪰ aⱼ iff. v(aᵢ , sₘ) ≥ (aⱼ , sₘ) where the state is sₘ

Question 8

Strong Dominance

Answer 8

aᵢ ≻ aⱼ iff. v(aᵢ , sₙ) ≥ v(aⱼ , sₙ), but there is at least one state sₙ where v(aᵢ , sₙ) > (aⱼ , sₙ).

Question 9

Maximin

Answer 9

Maximize the minimal value obtainable in an act.

“Choose the Best worst outcome”

Question 10

When using the Maximin principle, all we have to do is measure on __________ scales, since “___________” between the ordered outcomes is irrelevant.

Answer 10

ordinal; distance

Question 11

When the outcomes are ____________ (parrallel), the Maximin rules suggests ______________ between them.

Answer 11

equivalent; indifference

Question 12

Leximin

Answer 12

When the worst possibe outcome is parrallel to other outcomes, choose the second best outcome (3rd, 4th, nth…) that is as good as possible.

Question 13

Formalization of the Leximin Rule

Answer 13

aᵢ ≻ aⱼ iff. there is some integer n such that minⁿ(aᵢ) > minⁿ(aⱼ) and minm(aᵢ) = minᵐ(aⱼ) for all m<n.

Question 14

Maximax

Answer 14

Maximizing the maximal value obtainable in an act.

Rationality requires we believe the best outcome is as good as possible.

Question 15

Optimism-Pessimism Rule

Answer 15

asks decision maker to choose best and worst possible outcomes from a set of alternatives.
then
according to her degree of Optimism or Pessimism, choose an alternative.

Question 16

Degree of optimism can be represented using a real number 0-1, where α (alpha) = ___. Where α = 1, is ______________ _________________, and α = 0 is _______________ ______________. This means the ________ possible outcome can be represented by max(aᵢ) and the _________ possible outcome can be represented by min(aᵢ). We can therefore establish the function α * max(aᵢ) + (1 - α) * min(aᵢ).

Answer 16

1; maximal optimism; maximal pessimism; best; worst;

Question 17

Formalization of Optimism-Pessimism Rule

Answer 17

aᵢ ≻ aⱼ iff. α * max(aᵢ) + (1 - α) * min(aᵢ) > α * max(aⱼ) + (1 - α) * min(aⱼ)

Question 18

The concept of ______________ is relevant to rational decision making.

Answer 18

regret

Question 19

Minimax Regret Rule

Answer 19

minimize maximum amount of regret.

Question 20

How to Calculate Regret Values

Answer 20

Subtract best outcome value (row) by the value of outcome in question.

Question 21

Regret Matrix

Answer 21

matrix of regret values

Question 22

Principle of Insufficient Reason

Answer 22

transforms decisions under ignorance to decisions under risk by assigning probabilities to the states.

Question 23

To use the Principal of Insufficient Reason, we must assign ____________. So, if there is ‘n’ number of probabilities, we give each __________ of the world a probability of __/__.

Answer 23

probabilities; state; 1/n

Question 24

Randomizing Acts is decided by ____________, ______________, ________________ and _______________-______________ rule (so long as α is less than __/__).

Answer 24

Maximin; Leximin; Maximax; Optimism-Pessimism; 1/2

Question 25

2 Weak Points for Randomizing Acts

Answer 25

1) You can’t find expected value (EMV / EV).

• Were not applying probabilities of equal, let alone probabilities at all to the states.
  Makes the point that randomizing is kind of useless.

2) Once you’ve conducted a run of trials to get EV, by that time you should know what the probabilities of each outcome are.

• Then, there’s no need to randomize the acts if you’re already going to find out the frequency of the probabilities.