Decision Making Under Risk and Uncertainty - Chapter 7

These flashcards cover key concepts and theories related to decision making under risk and uncertainty as discussed in the lecture.

What assumption about decision-making does expected utility theory rely on?

That individuals will integrate possible outcomes with their current assets.

What is a RISKY decision?

A decision where specific outcomes occur only with a stated probability (probabilities are known).

What is decision making under UNCERTAINTY?

Decision making where probabilities of outcomes are NOT known — the more common real-world situation.

What is Expected Value (EV)?

The sum of each outcome multiplied by its probability. The 'mathematically optimal' choice according to EV Theory.

How do you calculate Expected Value?

Multiply each possible outcome by its probability, then add them all up. Choose the option with the highest result.

What is utility?

The subjective pleasure or usefulness a person gets from an outcome — not the same as the raw monetary value.

What is Expected Utility Theory?

The theory that rational people should choose the option that maximises their expected utility (not just expected value).

What is the St. Petersburg Paradox?

A coin-flip game where the prize doubles every flip until heads appears. Its expected value is mathematically infinite, yet people would only pay a small amount to play — showing people don't purely maximise expected value.

Who described the St. Petersburg Paradox, and when?

Daniel Bernoulli, originally written in 1738.

What does the St. Petersburg Paradox prove?

That people do NOT simply maximise expected value. At some point, more money adds very little extra satisfaction — demonstrating diminishing marginal utility.

What is diminishing marginal utility?

Each extra unit of money (or any good) adds less utility than the previous unit. More wealth is always better, but the gains shrink as you get richer.

Why does diminishing marginal utility make people risk-averse?

Because the pain of losing a sum of money is felt more intensely than the pleasure of gaining the same amount — the loss 'looms larger.'

What does the utility-of-wealth curve look like (Figure 7.1)?

A curve that rises steeply at low wealth levels and flattens out as wealth increases (concave shape).

What is Weber's Law?

The just-noticeable difference between two stimuli is a constant proportion of the stimulus magnitude, not a fixed amount.

What is Weber's Fraction?

The constant ratio obtained by dividing the difference threshold by the stimulus magnitude. It stays the same regardless of stimulus size.

Weber's Law example: 100g weight has a 2g threshold. What is Weber's Fraction, and what is the threshold for 200g?

Weber's Fraction = 2/100 = 0.02. Threshold for 200g = 0.02 × 200 = 4g.

How does Weber's Law relate to the utility function?

The utility curve has the same shape as magnitude-estimation curves — people respond to money proportionally, just as they do to physical stimuli.

What are the three major failures of Expected Utility Theory?

1. The fourfold pattern of risk attitudes (not always risk-averse)

2. The Allais Paradox (people don't maximise utility)

3. The Isolation Effect (people don't integrate outcomes with total assets)

What is the fourfold pattern of risk attitudes?

Gains + high probability → risk-averse; Losses + high probability → risk-seeking; Gains + low probability → risk-seeking; Losses + low probability → risk-averse.

Who discovered the fourfold pattern of risk attitudes?

Kahneman and Tversky (1979, 1992).

Why do people buy lottery tickets according to the fourfold pattern?

Because they are risk-seeking for gains with low probabilities — they overweight the small chance of a big win.

Why do people buy insurance according to the fourfold pattern?

Because they are risk-averse for losses with low probabilities — they overweight the small chance of a catastrophic loss.

What is the Allais Paradox?

A set of decision problems showing that people's preferences are logically inconsistent with utility maximisation — most prefer A over B, and D over C, even though this violates expected utility theory.

Who demonstrated the Allais Paradox, and when?

Maurice Allais, 1953.

What is Savage's Sure-Thing Principle?

Choices should be based only on attributes that DIFFER between options. Attributes that are identical in both options should not affect the decision.

How does the Allais Paradox violate the Sure-Thing Principle?

Options C and D are obtained by removing an 89% chance of €100m from both A and B. This shared element should not change preferences — but it does, reversing the majority choice.

What is the certainty effect?

The disproportionately large impact on preferences when outcomes switch between certainty and uncertainty (or vice versa). Certainty feels much more attractive than near-certainty.

What is the Isolation Effect?

People tend to ignore information about their existing assets and evaluate each decision in isolation — they do NOT integrate outcomes with total wealth as EU Theory requires.

Kahneman & Tversky's isolation effect experiment: Group 1 given $1,000, chooses between 50% chance of $1,000 more or $500 sure. What does most choose, and why is this surprising?

Most choose the sure $500 (84%). Surprising because EU Theory says they should integrate the $1,000 gift, making the options identical to the other group's — but framing as a gain makes them risk-averse.

What is Prospect Theory?

A psychological theory of decision making by Kahneman and Tversky (1979) that describes how people actually evaluate risky prospects — using a value function and decision-weighting function relative to a reference point.

Who developed Prospect Theory and when?

Daniel Kahneman and Amos Tversky, 1979.

What are the two stages of decision making in Prospect Theory?

1. The Editing Stage (structuring/simplifying the problem)

2. The Evaluation Stage (applying the value function and weighting function)

What happens during the Editing Stage in Prospect Theory?

Decision makers code potential outcomes as gains or losses relative to a reference point, simplifying the problem before evaluating it.

What is a reference point in Prospect Theory?

The baseline against which outcomes are judged as gains or losses. Usually the status quo, but can also be an expectation or aspiration.

How does the reference point differ from EU Theory's approach?

EU Theory always evaluates outcomes relative to total current wealth. Prospect Theory evaluates outcomes relative to a flexible reference point that can shift based on context.

Give an example of how an objective gain can feel like a loss due to the reference point.

Expecting a $5,000 bonus but receiving $3,000 — you gained $3,000 objectively, but your reference point (expectation) makes it feel like a $2,000 loss.

Describe the shape of the Prospect Theory value function (Figure 7.2).

An S-shaped curve: concave (bowing down) for gains on the right, convex (bowing up) for losses on the left. The loss side is steeper than the gain side.

What does it mean that the value function is concave for gains?

Diminishing sensitivity to gains — the difference between $0 and $100 feels bigger than the difference between $1,000 and $1,100.

What does it mean that the value function is convex for losses?

Diminishing sensitivity to losses — the first $100 loss hurts more than going from a $1,000 loss to a $1,100 loss.

What does the steeper slope of the value function for losses mean?

Loss aversion — losing $100 hurts roughly twice as much as gaining $100 feels good.

What is loss aversion?

The tendency for losses to feel more impactful than equivalent gains. A core feature of Prospect Theory's value function.

What is the decision-weighting function in Prospect Theory?

A function that transforms stated probabilities into decision weights — reflecting how much each probability level actually influences behaviour (not what people believe the probability to be).

Describe the shape of the probability weighting function (Figure 7.3).

A reverse S-shape: small probabilities are overweighted (curve is above the diagonal), large probabilities are underweighted (curve is below the diagonal), with steep sensitivity near 0 and 1.

What is subcertainty in Prospect Theory?

The property that all decision weights for a set of outcomes sum to LESS than 1 — meaning people globally discount probability.

Why do small probabilities get overweighted in the weighting function?

People are disproportionately sensitive to the possibility (vs. impossibility) of an event. A 1% chance feels like more than 1% of certainty.

What real-world behaviours does the overweighting of small probabilities explain?

The popularity of lottery tickets (small chance of huge gain) and insurance (small chance of catastrophic loss).

What is a framing effect?

When the same objective information, described in different words (e.g., as a gain vs. a loss), leads to different decisions — violating the invariance axiom of EU Theory.

What is the invariance axiom of EU Theory?

Logically equivalent descriptions of the same decision should yield the same preference — irrelevant changes in wording should not affect choice.

Describe the Asian Disease Problem and what it demonstrates.

600 people will die from a disease. Framed as 'lives saved' (gain frame), most choose the sure option (200 saved). Framed as 'deaths' (loss frame), most choose the risky option (1/3 chance nobody dies). Same outcomes, opposite choices — demonstrating framing effects.

What is the credit card framing example in the chapter?

Credit card lobbyists wanted price differences to be called a 'cash discount' rather than a 'credit card surcharge' — because a surcharge feels like a loss (worse), while a missing discount just feels like a foregone gain (better).

What brain regions are involved in framing effects?

Amygdala (emotional gut-reaction system, fires when going with the default framing) and the Anterior Cingulate Cortex or ACC (conflict monitoring, fires when overriding the gut feeling).

Who is LESS susceptible to framing effects?

People with higher cognitive ability (higher SAT scores) and those who enjoy effortful thinking — found by Stanovich & West (1998).

Does positive or negative framing lead to more cognitive processing?

Negative framing leads to more cognitive processing — slower response times, more brain activity, and greater disparity between current state and goal state.

What is the end-of-day effect in horse racing?

Bettors shift money away from favourites and toward long-shots in the last race of the day — because they frame their position as a 'loss' relative to breaking even, triggering risk-seeking behaviour.

What did studies of NYC cab drivers reveal about Prospect Theory?

Inexperienced drivers quit early on good days once they hit a daily earnings target (treating further earnings as less important), and stayed longer on bad days trying to 'make up' losses — consistent with a daily reference point.

What is the disposition effect in investing?

Investors hold on too long to losing stocks (avoiding realising a loss) and sell winning stocks too early (locking in gains) — a consequence of loss aversion.

What did Odean (1998) find about the disposition effect?

One year after investors sold winning stocks, those stocks still outperformed the losing stocks investors had held on to — proving the disposition effect leads to objectively worse financial decisions.

What did Montague (2006) argue about the brain and valuation?

The nervous system needs a common internal currency to compare the value of completely different goals (food, water, safety, etc.) and convert them to a single scale to guide behaviour.

What role do dopamine neurons play in reward valuation?

Midbrain dopamine neurons in the ventral tegmental area (VTA) fire when an unexpected reward occurs, encoding reward prediction errors — the difference between what was expected and what was received.

What is a reward prediction error?

The difference between the reward you expected and the reward you actually got. Dopamine signals this error: unexpected reward = spike; expected reward = flat; expected reward missing = dip below baseline.

How does the dopamine reward prediction error system relate to Prospect Theory?

Both are fundamentally about DEVIATIONS from a reference point (expectation). The brain doesn't just register reward — it registers whether the reward was better or worse than expected.

What is Decision by Sampling Theory?

A theory (Stewart, 2016) proposing that when making decisions, people compare attribute values (like monetary amounts or probabilities) against previously encountered values sampled from memory.

How does Decision by Sampling explain loss aversion?

There are more small losses than small gains in everyday bank records (a power law). So losses are more frequently sampled from memory, making people more sensitive to them.

How does Decision by Sampling explain the shape of the probability weighting function?

Small and large probabilities are over-represented in the real world relative to middle probabilities — so memory-based sampling makes the brain weight them more heavily, producing the S-shaped weighting function.

What is Risk Sensitivity Theory?

A theory derived from animal foraging biology: organisms shift between risk-averse and risk-seeking behaviour depending on whether their current resources are above or below a survival threshold.

When does Risk Sensitivity Theory predict risk-seeking behaviour?

When you are BELOW your survival threshold — you need to take risks to survive. Being 'in the loss domain' biologically triggers risk-seeking.

When does Risk Sensitivity Theory predict risk-averse behaviour?

When you are ABOVE your survival threshold — no need to gamble when you have enough. Being 'in the gain domain' triggers caution.

What is the Two-Stage Model of decision making under uncertainty?

A model combining Support Theory (for probability assessment when probabilities are unknown) with Cumulative Prospect Theory (for evaluating outcomes with distorted weighting).

What is Support Theory?

A theory of probability judgment stating that the more ways you can imagine an event happening (more cognitive 'support'), the higher probability you assign to it — even for objectively equivalent events.

What is Cumulative Prospect Theory?

An updated version of Prospect Theory (Tversky & Kahneman, 1992) that applies the value and weighting functions cumulatively across multiple outcomes, making it usable for real-world uncertainty.

What are process models of decision making?

Models concerned with the STAGES of thinking that lead to a decision — not just predicting the final choice, but describing how the decision is reached step by step.

What is Decision Field Theory?

A process model that treats decision making as a dynamic, evolving process — preference accumulates over time as attention shifts between different attributes of the options, until one reaches a threshold.

What is the Priority Heuristic?

A simple step-by-step shortcut for decision making: (1) compare minimum outcomes, (2) if still undecided, compare probabilities of minimums, (3) if still undecided, compare maximum outcomes. Stop as soon as a step gives a clear enough answer.

What are the three steps of the Priority Heuristic in order?

1. Compare the minimum (worst-case) outcomes

2. Compare the probabilities of those minimums

3. Compare the maximum (best-case) outcomes

What makes the Priority Heuristic significant?

Despite being a simple shortcut (not full calculation), it accurately predicts many human choices — including violations of Expected Utility Theory like the Allais Paradox.

Who are Kahneman and Tversky?

Daniel Kahneman and Amos Tversky — psychologists who developed Prospect Theory (1979) and the fourfold pattern of risk attitudes. Kahneman later won the Nobel Prize in Economics (2002).

Who is Richard Thaler and what is his contribution to this chapter?

An economist who identified framing effects in real-world consumer behaviour (e.g., the credit card 'surcharge vs. discount' example) and developed behavioural economics. Won the Nobel Prize in 2017.

Who is Maurice Allais?

French economist who demonstrated the Allais Paradox (1953), showing people systematically violate Expected Utility Theory's sure-thing principle.

Who is Daniel Bernoulli?

18th-century mathematician who introduced the concept of utility and diminishing marginal utility to explain the St. Petersburg Paradox (1738).

Who is Ernst Weber?

German physiologist (1795–1878) after whom Weber's Law is named — the discoverer that difference thresholds are proportional to stimulus magnitude.