Chapter 3: Decisions Under Ignorance Flashcards
Ignorance
Decision maker
1) knows outcome and what outcome may result in.
2) can’t assign a probability states corresponding to outcomes.
The _____________ principle states that ______________ acts (where one act is clearly worse than another) must ____ be chosen.
Dominance; dominated; NOT
aᵢ ≻ aⱼ
Act “i” is better than Act “j”
This means one is rationally required / ought to choose act i
aᵢ ⪰ aⱼ
Act i is at least as good as Act j
aᵢ ~ aⱼ
Act i and Act j are equally rational.
v(a₁, s₁) = 1
The value of doing act 1 in state 1 equals, should state 1 be the true state of the world, is 1 (ordinal ranking).
Weak Dominance
aᵢ ⪰ aⱼ iff. v(aᵢ , sₘ) ≥ (aⱼ , sₘ) where the state is sₘ
Strong Dominance
aᵢ ≻ aⱼ iff. v(aᵢ , sₙ) ≥ v(aⱼ , sₙ), but there is at least one state sₙ where v(aᵢ , sₙ) > (aⱼ , sₙ).
Maximin
Maximize the minimal value obtainable in an act.
“Choose the Best worst outcome”
When using the Maximin principle, all we have to do is measure on __________ scales, since “___________” between the ordered outcomes is irrelevant.
ordinal; distance
When the outcomes are ____________ (parrallel), the Maximin rules suggests ______________ between them.
equivalent; indifference
Leximin
When the worst possibe outcome is parrallel to other outcomes, choose the second best outcome (3rd, 4th, nth…) that is as good as possible.
Formalization of the Leximin Rule
aᵢ ≻ aⱼ iff. there is some integer n such that minⁿ(aᵢ) > minⁿ(aⱼ) and minm(aᵢ) = minᵐ(aⱼ) for all m<n.
Maximax
Maximizing the maximal value obtainable in an act.
Rationality requires we believe the best outcome is as good as possible.
Optimism-Pessimism Rule
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.
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).
1; maximal optimism; maximal pessimism; best; worst;
Formalization of Optimism-Pessimism Rule
aᵢ ≻ aⱼ iff. α * max(aᵢ) + (1 - α) * min(aᵢ) > α * max(aⱼ) + (1 - α) * min(aⱼ)
The concept of ______________ is relevant to rational decision making.
regret
Minimax Regret Rule
minimize maximum amount of regret.
How to Calculate Regret Values
Subtract best outcome value (row) by the value of outcome in question.
Regret Matrix
matrix of regret values
Principle of Insufficient Reason
transforms decisions under ignorance to decisions under risk by assigning probabilities to the states.
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 __/__.
probabilities; state; 1/n
Randomizing Acts is decided by ____________, ______________, ________________ and _______________-______________ rule (so long as α is less than __/__).
Maximin; Leximin; Maximax; Optimism-Pessimism; 1/2
2 Weak Points for Randomizing Acts
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.
