Chapter 9: Causal vs. Evidential Decision Theory Flashcards
Beliefs about ______________ ______________ play a significant role in determining what we __________________ think is the ____________ thing to do.
causal processes; intuitively; rational
Example of Casual Processes
Newcomb’s Problem
Newcomb’s Problem
- There is a predictor whose predictions are correct 99% of the time.
- You are faced with 2 boxes:
- Box 1 contains $1000 and (You know this, the box is transparent)
- Box 2 contains either $1M or $0 (the box is not transparent)
- Your choices are as follows:
- Alt. 1: Choose BOTH boxes ($1000 and $0 or $1M)
- Alt. 2: Choose ONLY box 2 ($0 or $1M)
- If the predictor predicts that you will only choose Box 2, she will place $1M in the box, but otherwise, she will put nothing in there ($0). She knows you know this.
- REMEMBER, this predictor has been right 99% of the time.
Robert Nozick’s Response
Dominance Principle
You should definitely choose BOTH boxes:
- You’ll for sure get $1000 and whatever is in Box 2, be it nothing or $1M.
- The $1M either IS or IS NOT in Box 2. The Predictors placed either $1M or nothing in the box based on her prediction, before you chose a box.
- Her prediction has nothing to do with the fact that $1M is either in the box or not.
- The predictor doesn’t have “magical powers” to adjust circumstances so that $1M appears in Box 2 if you decide to choose only Box 2.
Reply to Nozick’s Approach (See notes for Decision Matrix)
Maximizing Expected Utility
Technically, wouldn’t be have a better chance of becoming millionares if we chose ONLY Box 2?
- Think about it, taking into account everything that problem poses, the predictors prediction feasability has consistently been 99%.
- If the decision maker predicted you would choose only Box 2, and hence placed $1M in the box, and you did infact only Box 2, she would be correct.
- It follows that if she predicted you would choose both boxes, and hence placed nothing in Box2, and you selected both boxes, she would be correct.
- This would technically mean we have a higher chance at becoming millionares if we chose only Box 2.
Problem w/ Responses to Newcomb’s Problem
We have to different principles of rational decision making telling us to take 2 entirely different courses of action.
The Dominance Principle recommends we take BOTH boxes.
The Principle of Maximizing Expected Utility supposes we should take ONLY box 2.
Source of Misunderstanding 1) and its Response
We’re not suppose to know the predictive power of this being. Surely it’s impossible for a single being to be able to make predictions that are 99% correct all the time.
Response: This isn’t helpful. Decision makers find ways of making rationals decisions by IMAGINING that a being liket that could exists. Also, in this proposal, we should accept the predictive power of this being. Let’s we ran an experiment with a select number of people, and because this being is almost certainly right all the time, everyone who 1 Box became millionares, whereas those selected both boxes only receieved thousands of dollars.
Source of Misunderstanding 2) and its Response
“The predictor has magical powers.”
Response: No she doesn’t, she’s just a really good predictor.
Causal Decision Theory
Decision maker’s beliefs on causal processes should remain fixed in decision making processes, and should choose the best alternative according to their beliefs.
The ______________ _______________ of the world is going _________________, and can’t be effected by things in the ______________.
causal structure; forward; past
What would Causal Decision Theory tell us to do regarding Newcomb’s Problem, and why?
Causal Decision Theory says take both boxes.
- Based on the predictor’s prediction, she’s either going to place or not place $1M in Box 2. There’s nothing I can do NOW to change the probability that I may recieve $1M (which has already been decided, hence it’s a past event).
- But, as the rule tells us, I choose the best alternative, and take both boxes because I’ll certainly get $1000.
Review Smoking / Lung Cancer Problem (See notes)
- More to do with Causal Decision Theory.
- Let’s say you’re a rational decision maker/regular smoker, and a new piece of knowledge surfaces that there is a defect among people that cause Lung Cancer and the drive (impulse) to smoke.
- Rationally speaking, this shouldn’t change your decision to smoke or not (your causal decision beliefs should remain the SAME).
- (Ludicrous as it sounds, the problem tells us it’s the defect that causes Lung Cancer, for our purposes, smoking doesn’t actually cause cancer).
- Any decision / act I make NOW will have no affect on me getting or not getting lung cancer, it’s the defect (state of world).
- The only thing that smoking does provide is a small benefit of enjoyment that comes with smoking.
Decision Maker:
Defect No Defect Smoke Lung Cancer / Enjoyment No Lung Cancer / Enjoyment Not Smoke Lung Cancer / No Enjoyment No Lung Cancer / No Enjoyment
To better understand ____________ ______________ theory, we need to ______________ it.
causal decision; formalize
How to Formalize the statement, “If the decision maker did X, then Y would be the case.”
X◻→Y
What does “p(X◻→Y)” mean? (See Notes for Examples)
“probability of decision maker doing X, and getting Y in result is true.”
