001 halpern 1 DT under certainty

001 halpern 1 DT under certainty - Decision Theory Decision...

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

Decision Theory Decision theory is about making choices It has a normative aspect what “rational” people should do . . . and a descriptive aspect what people do do Not surprisingly, it’s been studied by economists, psychol- ogist, and philosophers. More recently, computer scientists have looked at it too: How should we design robots that make reasonable decisions What about software agents acting on our behalf agents bidding for you on eBay managed health care Algorithmic issues in decision making This course will focus on normative aspects, informed by a computer science perspective. 1 Axiomatic Decision Theory Standard (mathematical) approach to decision theory: Give axioms characterizing reasonable decisions Ones that any “rational” person should accept Then show show that these axioms characterize a par- ticular approach to decision making For example, we will discuss Savage’s axioms that characterize maximizing expected utility. An issue that arises frequently: How to represent a decision problem 2 Choice Under Certainty Assumption: you’re given a set X of objects. You have to state which one you want most More generally: you give a preference order among objects in X Notation: x follows y means x is strictly preferred to y There’s no uncertainty: you get what you choose. Goal: to understand reasonable properties of a pref- erence order Example : X = { a, b, c } , b follows a , a follows c , and c follows a . Are such cyclic preferences reasonable? Would a rational person have such preferences? 3 Axioms for Choice Under Certainty Asymmetry: If x follows y then y negationslash follows x . Negative Transitivity: If x negationslashfollows y and y negationslashfollows z then x negationslash follows z Transitivity: If x follows y and y follows z , then x follows z . Proposition: Asymmetry + NT imply Transitivity. Proof: Suppose that x follows y , y follows z , and x negationslashfollows z . By asymmetry, we have z negationslashfollows y . By NT, we have x negationslashfollows y contradiction. Is NT a good normative or descriptive property? Proposition. The binary relation follows is negatively tran- sitive iff x follows z implies that, for all y X , x follows y or y follows z . (Proof in Kreps) NT comes pretty close to saying that follows is a total order For all x , y , either (1) x follows y
Image of page 1

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

Image of page 2
This is the end of the preview. Sign up to access the rest of the document.
  • Fall '06
  • SEN, preference relation

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern