Decision analysis Study Guide

📖 Core Concepts Decision Analysis – a formal discipline that blends philosophy, methodology, and practice to tackle important decisions. Maximum Expected‑Utility Axiom – the recommended action is the one that gives the highest expected utility (EU). Framing – front‑end process that creates the opportunity statement, boundary conditions, success measures, decision hierarchy, strategy table, and action items. Value‑Focused Thinking – a qualitative tool used during framing; it helps identify what truly matters before any numbers are introduced. Graphical Representations – influence diagrams and decision trees depict alternatives, uncertainties, and outcomes relative to the decision‑maker’s objectives. Subjective Probabilities – probabilities supplied by the decision maker to represent uncertainty. Utility Functions – numerical representations of a decision maker’s attitude toward risk (higher utility = more preferred). Multi‑Attribute Value/Utility Functions – combine several objectives into a single score; utility version incorporates risk. Uncertain Aspiration Level (Target) – an alternative to a utility function: maximize the probability of reaching a desired outcome level. Prescriptive vs. Descriptive – prescriptive research seeks the optimal decision under rationality axioms; descriptive research explains how people actually decide. --- 📌 Must Remember Decision analysis prescribes actions by maximizing expected utility (or probability of hitting an aspiration level). EU formula: $$EU = \sum{i} pi \, u(xi)$$ where \(pi\) = subjective probability of outcome \(xi\), \(u(\cdot)\) = utility. Framing produces a decision hierarchy and a strategy table before any quantitative work. Utility ≠ Money – utility captures risk preferences, not just dollar values. Multi‑attribute utility theory is the gold‑standard benchmark for evaluating other methods. Decision analysis can handle intangible factors (e.g., reputation, employee morale) via value functions. Prescriptive = “what should be done”; Descriptive = “what is done”. No axiomatic prescriptive theory exists for group or public‑policy decisions—the theory is individual‑centric. --- 🔄 Key Processes Frame the Problem Write an opportunity statement. Define boundary conditions and success measures. Build a decision hierarchy and a strategy table. List concrete action items. Select a Graphical Model Use an influence diagram for compact, high‑level view. Use a decision tree when the sequence of events matters. Elicit Quantitative Elements Assign subjective probabilities to uncertain events. Define a utility function (or multi‑attribute utility/value function). If utility elicitation is impractical, set an aspiration level and estimate the probability of achieving it. Compute Expected Utility For each alternative, calculate \(EU = \sum pi u(xi)\). If using aspiration level, compute \(P(\text{achieve target})\). Select the Optimal Alternative Choose the alternative with the highest EU (or highest target‑achievement probability). Translate Result into Insight Communicate the recommendation and the underlying trade‑offs to stakeholders. --- 🔍 Key Comparisons Prescriptive vs. Descriptive Prescriptive: seeks optimal decisions via rationality axioms. Descriptive: explains real‑world decision behavior, regardless of optimality. Influence Diagram vs. Decision Tree Influence Diagram: concise, shows relationships among variables. Decision Tree: explicit sequence of choices and chance events. Utility Function vs. Aspiration‑Level Probability Utility: captures risk attitude across all outcomes. Aspiration Level: focuses on probability of meeting a target, bypassing full utility curve. Multi‑Attribute Value vs. Multi‑Attribute Utility Value: risk‑neutral aggregation of multiple objectives. Utility: adds risk attitudes to the multi‑objective aggregation. Individual Decision Analysis vs. Group Decision Context Individual: has a solid axiomatic foundation. Group: lacks a comparable prescriptive theory; methods are largely ad‑hoc. --- ⚠️ Common Misunderstandings “Decision analysis only works with dollars.” → It can quantify intangible factors via value functions. “Utility is the same as monetary payoff.” → Utility reflects preferences and risk, not just cash. “Group decisions have the same axiomatic basis as individual decisions.” → No formal prescriptive theory exists for groups. “Subjective probabilities must be objectively verified.” → They are the decision maker’s personal assessments. “Value‑focused thinking is a quantitative technique.” → It is purely qualitative, used before numbers. --- 🧠 Mental Models / Intuition Weighted Scoreboard: Imagine each possible outcome gets a “score” (utility) and a “chance” (probability). The decision’s overall worth is the average score you’d expect to earn—pick the highest‑scoring option. Framing as Blueprint: Treat framing like drafting a building plan; you first decide where the building sits (boundaries, objectives) before choosing materials (probabilities, utilities). --- 🚩 Exceptions & Edge Cases Intangible Variables: Even without natural units, assign a value function (e.g., reputation score) to include them in EU calculations. Aspiration‑Level Substitution: When eliciting a full utility function is infeasible, maximize the probability of achieving a pre‑set target instead. Group Decisions: Apply individual decision‑analysis tools only as advisory aids; no formal axiomatic group model exists. --- 📍 When to Use Which | Situation | Recommended Tool / Approach | |-----------|-----------------------------| | Multiple, interdependent objectives and risk matters | Multi‑attribute utility function | | Multiple objectives but risk‑neutral | Multi‑attribute value function | | Need a quick, high‑level view of relationships | Influence diagram | | Decision involves a clear sequence of choices & chance events | Decision tree | | Eliciting a full utility curve is too time‑consuming | Aspiration‑level probability method | | Early stage, before numbers are available | Value‑focused thinking (qualitative) | | Individual decision maker with clear preferences | Full prescriptive decision analysis | | Group or public‑policy setting | Use decision‑analysis outputs as informational support only | --- 👀 Patterns to Recognize “Trade‑offs among multiple objectives” → look for multi‑attribute value/utility formulations. Mention of “subjective probabilities” → signals a quantitative model is being built. “Maximum expected‑utility” or “maximizes probability of achieving the aspiration level” → the decision rule is being applied. Framing language (opportunity statement, boundary conditions, success measures) → indicates the front‑end process. References to intangible factors → expect a value‑based (non‑monetary) representation. --- 🗂️ Exam Traps Distractor: “Decision analysis only uses monetary outcomes.” → Wrong; intangible factors are accommodated via value functions. Distractor: “Group decisions can be solved with the same axioms as individual decisions.” → Incorrect; no comparable prescriptive theory for groups. Distractor: “Expected utility is simply the expected monetary value.” → Misleading; utility transforms monetary outcomes based on risk attitude. Distractor: “Value‑focused thinking requires probability estimates.” → False; it is a qualitative method used before quantitative analysis. Distractor: “The optimal decision always maximizes the probability of the most likely outcome.” → Incorrect; optimality is defined by maximizing expected utility (or target probability), not the most likely single outcome.