Chapter 20 – Decisions Involving Uncertainty (Vocabulary Flashcards)

Uncertainty & Decision-Making Context

• Uncertainty is pervasive; you encounter it when outcomes aren’t guaranteed.
  • Everyday examples: online shopping fit, car accidents, long-term relationships, parenting satisfaction, stock returns.
• Central question: How can we make good choices despite unknown consequences?
• Four analytic pillars introduced:
  • Understanding Risk (probabilities & payoffs)
  • Diminishing Marginal Utility
  • Risk-Reward Trade-off
  • Expected Utility

Risk: Probabilities & Payoffs

• Risk = a complete list of possible outcomes plus the probability of each.
  • Example investment: 50 % chance to gain \$20,000, 50 % chance to lose \$20,000.
• Fair bet: a gamble whose expected monetary value is zero.
  • E[\text{Payoff}] = 0 because positive and negative payoffs cancel on average.

Risk Aversion

• Definition: Dislike of uncertainty that leads to rejecting fair bets.
• Key insight: People evaluate gambles using utility, not money.
• Cost–Benefit Analysis for the Risk-Averse
  • Monetary payoffs → translate into changes in utility.
  • A fair monetary bet can still be a bad utility bet if the disutility of loss > utility of gain.

Utility Concepts

• Utility (U): numerical measure of well-being.
• Marginal Utility (MU): additional utility from an extra dollar.
• Diminishing Marginal Utility (DMU): MU{n+1} < MUn; each extra dollar matters less.
  • Explains risk aversion: losing \$20k hurts more than gaining \$20k helps.

Graphical Intuition

• Utility curve slopes upward but flattens at higher wealth.
  • Gain region: small vertical rise.
  • Loss region: comparatively larger vertical drop.

Risk-Reward Trade-off

• Even risk-averse people accept risk if rewards are high enough.
  • Original fair bet: ±\$20k → reject.
  • New bet: +\$30k / –\$10k with 50 % probability each → accept because U{gain} > U{loss}.
• Practical determinants of acceptance:
  • Size of reward, size of stake, individual degree of risk aversion.

Heterogeneity in Risk Aversion

• Temperament & life situation influence curvature of utility curve.
  • Example: Imani (mildly risk-averse) vs. Lucas (highly risk-averse) faced with same +\$30k/–\$10k gamble.
  • Imani’s flatter utility curve → accepts; Lucas’s steeper initial slope → rejects.

Expected Utility Framework

• Expected Utility (EU): probability-weighted average utility across outcomes.
  • General formula: EU = \sum{i} pi \times U(W_i)
• Investment illustration:
  • Current wealth \$30k → U(30k)=5.
  • 40 % chance wealth rises to \$50k, U(50k)=7.
  • 60 % chance wealth falls to \$15k, U(15k)=3.
  • EU = 0.4\times7 + 0.6\times3 = 4.6 < 5 ⇒ reject investment.
• Key takeaway: Choose the option with higher expected utility, not higher expected money.

Strategies for Reducing Risk

Five practical approaches, remembered as R-D-I-H-I (Risk spreading, Diversification, Insurance, Hedging, Information):

1. Risk Spreading

• Break one large stake into many tiny stakes distributed across people.
  • Large investment becomes 1,000 shares × \$100 each; each shareholder risks \$100, not \$100,000.
• Behavioral guideline:
  • Be risk-averse on large stakes, nearly risk-neutral on small stakes.

2. Diversification

• Combine many small, uncorrelated risks.
  • “Don’t put all eggs in one basket.”
  • Effective only when payoffs are not closely related (e.g., mix tech, utilities, real estate stocks).
• Limits: Systematic risk (economy-wide events) cannot be diversified away.

3. Insurance

• Contract: pay a premium to receive compensation if a specified loss occurs.
• Actuarially fair policy: expected payout = expected premiums (E[\text{Wealth}] unchanged).
• Buy insurance when: (i) policy close to actuarially fair, (ii) you’re highly risk-averse, (iii) stakes are large.

4. Hedging

• Take on an offsetting risk so gains in new position counterbalance losses in original position.
  • Examples: buy oil stocks to hedge gasoline bill; acquire computer skills to hedge job automation risk.
• Anti-hedge: owning your employer’s stock—job loss and investment loss coincide.

5. Gathering Information

• More data reduces uncertainty, especially valuable for high-stakes decisions.
  • Check weather app before dressing.
  • Pay for vehicle inspection before buying used car (adverse selection mitigation).
  • Market research before launching business.

Behavioral Economics: Why People Err Under Uncertainty

• Incorporates psychological insights into economic analysis (Richard Thaler’s contribution).
• Dual-System Cognition (Daniel Kahneman):
  • System 1: fast, automatic, intuitive.
  • System 2: slow, deliberate, analytical.
• Good decision-makers know when to override System 1 with System 2.

Common Biases & Pitfalls

1. Overconfidence
   • Tendency to overrate accuracy of forecasts → understate risk.
   • Remedy: deliberate System 2 checks, humility (Gandhi quote).
2. Availability Bias
   • Overweigh memorable events (shark attacks, plane crashes) → misjudge probabilities.
   • Question: more words with ‘r’ as 1st letter or 3rd letter? Easy recall distorts answer.
3. Anchoring Bias
   • Initial number (anchor) skews subsequent estimates.
   • Auditor study: anchor at 200/1000 → higher fraud prevalence estimates than anchor at 10/1000.
4. Representativeness Bias
   • Judge probability by similarity to stereotype; neglect base rates.
   • “Sarah is shy…” → most guess librarian, ignoring that teachers vastly outnumber librarians.
5. Focusing Illusion
   • Overemphasize salient aspects and ignore others when predicting happiness.
   • Students overrate California life quality due to weather, overlooking friends, family, cost.
6. Loss Aversion
   • Losses feel larger than equivalent gains; can lead to overly cautious choices.
   • Recommendation: emphasize net payoffs, not framing as losses.

Summary Checklist for Better Decisions

• Evaluate both payoffs and probabilities carefully:
  • Recognize & correct Overconfidence.
  • Counter Availability by seeking statistics.
  • Re-anchor using objective data.
  • Apply base-rate information to combat Representativeness.
  • Widen perspective to escape Focusing Illusion.
  • Reframe outcomes symmetrically to reduce Loss Aversion.

Master Formulae & Numerical References

• Fair bet: E[\text{Money}] = \sum pi \times xi = 0
• Expected Utility: EU = \sum{i=1}^{n} pi \times U(W_i)
• Actuarially Fair Insurance: \text{Premium} = E[\text{Payout}] (so E[\text{Wealth}] unchanged but variance ↓).

Integrated Key Take-Aways

• Every choice in life involves risk; risk aversion originates from diminishing marginal utility.
• Reject fair bets if utility loss exceeds utility gain, accept risk when reward sufficiently compensates.
• Manage risk with five tools: Risk spreading, Diversification, Insurance, Hedging, Information.
• Behavioral biases systematically distort perceived probabilities and payoffs; conscious System 2 reasoning can mitigate errors.
• Use Expected Utility, not intuition, as the decision criterion to navigate uncertainty rationally.