Chapter 8: Bayesianism and Pragmatic Arguments Flashcards
Bayesianism
Has an epistemic and deliberative Component.
Epistemic Component: What one’s state of mind ought to be like.
Deliberative Component: How one ought to act given one’s state of mind.
The Epistemic Component basically says one can believe ____________ one wants to believe as long as these _____________, or _____________ of _____________, are ______________ permissible, can be represented by a _________________ probability function, and those ___________ can be updated in accordance with ___________ ______________.
whatever; beliefs; combinations; beliefs; rationally; subjective; beliefs; Bayes’ Theorem.
Bayesian Epistemology
Provides structural restrictions on what one should believe, and how to revise beliefs in light of new information.
Bayesians maintain that all ______________ come in ________________, and, in that vain, ______________ probability is good account of how _____________ of ___________ ought to be revised.
beliefs; degrees; subjective; degrees; belief
The correct way for one to update their beliefs is using…
Bayes’ Theorem.
Issue of Bayesian Epistemology and how it can be resolved (See Notes)
Issue: How to caclulate prior probabilities.
Resolution: Even if 2 people have different priors, after enough experiments / iterations, the priors will converge towards eachother (such that they will essentially be the same prior/ close to the same).
Rational decision makers act AS IF they maximize subjective expected utility. What does this mean?
A decision maker doesn’t prefer an uncertain prospect over another BECAUSE she judges the outcomes of the uncertain prospect to be more favorable than the outcomes of another offer.
Her preferences are organized by structural axioms, giving her preferences well-organized structure, AS IF applying utility and probability function to her preferences
…such that a more preferred preference will always have a higher expected utility and less preferred preference will always have a lower expected utility.
Reasoning backwards, we realize the structural axioms gave the preferences a well organized structure, which allowed us to reason the preferences being described AS IF subjective probability and utility functions were used, which would be consistent with Maximizing Expected Utility.
Ordering Axiom
When there are 2 preferences, the decision maker must be able state a clear and unambiguous preference over another.
- All such preferences are Asymetric and Transitive.
Remember, the Ordering Axiom doesn’t actually inform the decision maker of what _____________ they should _____________, they merely provide the necessary ______________ based on the _______________ you have already ____________.
preferenes; have; constraints; preferences; formed
E.g. Odering axiom won’t tell you to prefer red wine to white wine, they’ll just tell you that if you prefer red to white, then you must not prefer white to red (asymmetry).
One’s preferences can be identified through ______________ _____________–it ultimately comes down to doing the act. This means that, among 2 unknown prospects, if one chooses ______ of the unknown prospects over __________, they necessarily ____________ the chosen prospect.
choice behavior; one; another; prefer
Extracting Subjective probabilities and utilities from preferences over uncertain prospects GIVEN that they can somehow establish that the agent considers Event 1) and Event 2) to be equally likely states.
An agent considers R and ¬R equally probable, when they are indifferent between the prospect of (i) getting 200 units of utility if R occurs and 100 units of utility if ¬R occurs, AND (ii) getting 100 units of utility of ¬R occurs and 200 units of utility if R occurs.
Central Components to Bayesian Decision Theory
1) Transivity Axiom: If x≻y, and y≻z, then x≻z.
2) Completeness Axiom: x≻y or y≻x or x~y
3) Independence Axiom: If x≻y, then xpz ≻ ypz
How do we determine if the Bayesian preference axioms should be accepted?
They have to be Pragmatically Justified.
For the Bayesian preference axioms to be ____________ ________________, they have to follow _______________ of ________________; they have to _____________ and ______________.
Pragmatically Justified; principles; rationality; practical; realistic
We say Bayesian preference axioms need to be ________________ _________________ because though at face value, these axioms have _____________ level appeal, there are cases in which they are proven to not be _______________.
pragmatically justified; surface; pratical
