QR 26 Choice and Chance: The Mathematics of Decision Making Outline

Introduction

Everyone makes decisions all the time, but few study how to make good ones. Descriptive, normative, prescriptive perspectives on decision making. Behavioral anamolies--e.g., anchoring, framing bias, retrievability bias, etc.

Unit I: The Logic of Preferences

A weak preference order ("A is at least as good as B") is complete and transitive. A strong preference order ("A is preferred to B") is negatively transitive and acyclic. Good preference orders obey the axiom of Independence of Irrelevant Alternatives. Measurement scales--nominal, ordinal, interval, ratio.

Unit II: Tradeoffs Under Certainty

The PrOACT (Problem, Objectives, Alternatives, Consequences, Tradeoffs) method of solving problems under certainty. Equal Swaps. Eliminating dominated alternatives and equally-met objectives. Value functions are useful because they convert preference information to inequalities of numbers. When the attributes are preferentially independent, an additive value function can be used. An application of preferential independence (of money in any given year from money in other years) leads to the Net Present Value of a cash flow.

Unit III: Optimization and Mathematical Programming

In many cases, a linear additive value function is possible, and we seek to maximize or minimize it. Choice variables, constraints, the corner principle. Sensitivity Analysis: Shadow prices and coefficient ranges.

Unit IV: Judgement and Decisions Under Uncertainty

Objective Orientation: Classical and Frequentist perspectives on probability. Canonical Probabilities for dice rolls, coin flips, urn drawings, etc., The Binomial Distribution. Subjective Orientation: Bayesian perspective, based on degrees of belief. The Sapling. Substitution of BRLTs reflects utility. Behavioral Anomalies--Allais, Ellsberg, and Russian Roulette paradoxes.

Unit V: Inference, the Value of Information, and Sequential Choice

Moving from the one-node decision tree to the many-node tree. Conditional Probability. Bayes' Theorem and its applications. Revising probabilities. Expected Value of Perfect Information and Expected Value of Sample Information.

Unit VI: Perspectives and Extensions

Basic Game Theory and Negotiation Theory