576wk3a_x4

576wk3a_x4 - The rest of the course Subtleties involved...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The rest of the course Subtleties involved with maximizing expected utility: • Finding the right state space: ◦ The wrong state space leads to intuitively incorrect answers when conditioning • Taking causality into account ◦ If you don’t, again you have problems • Computational issues: ◦ Computing probabilities efficiently using graphical representations ◦ Computing utilities efficiently ◦ Eliciting utilities efficiently • Problems with maximizing expected utility ◦ Effects of framing ◦ Ellsburg paradox, Allais paradox ◦ Dealing with large state/outcome spaces • (Possibly) some discussion on alternatives to proba- bility for representing belief (and how this impacts decision making) • Current research by Blume, Easley, Halpern 1 Savage: Summary Prof. Blume showed that if your preferences satisfy pos- tulates A1-A5, then that determines a qualitative proba- bility triangleright on events: • A triangleright B if A is more likely than B (where A and B are sets of states. With two more (arguably less plausible) axioms, A6 and A7, Savage is able to prove his major theorem: Theorem: If follows is a preference order on acts satisfying A1–A7, then there exists a probability Pr on states and a utility u on acts such that f follows g iff EU Pr ( f ) > EU Pr ( g ) . Moreover, Pr is unique and u is unique up to affine trans- formations. 2 Savage: Interpretation • Savage’s theorem says that, if a decision maker obeys Savage’s postulates, she is acting as if she has a prob- ability on states and a utility on outcomes, and is maximizing expected utility. • Note surprisingly Pr( A ) = 0 iff A is null • Pr extends the qualitative probability determined by A1–A5. • For each set B , follows B also satisfies Savage’s postulates; Pr( · | B ) is the probability determined by this pref- erence order. Today’s topic: Savage assumes you’re handed a state space. • How do we now we have the right state space? • The wrong state space leads to funny results. • The Blume-Easley-Halpern approach avoids states al- together. 3 Three-Prisoners Puzzle Computing the value of information involves condition- ing. Conditioning can be subtle ... Consider the three-prisoner’s puzzle: • Two of three prisoners a , b , and c are chosen at ran- dom to be executed, • a ’s prior that he will be executed is 2/3. • a asks the jailer whether b or c will be executed • The jailer says b . It seems that the jailer gives a no useful information about his own chances of being executed. • a already knew that one of b or c was going to be executed But conditioning seems to indicate that a ’s posterior prob- ability of being executed should be 1 / 2....
View Full Document

This homework help was uploaded on 02/19/2008 for the course ECON 4760 taught by Professor Blume/halpern during the Fall '06 term at Cornell.

Page1 / 7

576wk3a_x4 - The rest of the course Subtleties involved...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online