Chapter 11 Quiz: Information Aggregation Theory

Instructions: Select the best answer for each question. Some questions may have multiple correct answers; choose the most correct or complete option.

Question 1

What is the Hayek Hypothesis as applied to prediction markets?

• (a) Markets always produce the correct outcome
• (b) Market prices aggregate dispersed private information into a collective probability estimate that reflects more knowledge than any single trader possesses
• (c) Government regulation is necessary for markets to function
• (d) Prices are always equal to the true probability of the event

Answer: (b)

Explanation: The Hayek Hypothesis states that market prices serve as information carriers that synthesize the dispersed, partial knowledge of individual participants. This does not mean prices are always perfectly correct (ruling out (a) and (d)), nor does it require government regulation (ruling out (c)). The key insight is that the price reflects more information than any single participant has.

Question 2

Under the weak form of the Efficient Market Hypothesis, which of the following trading strategies should NOT be profitable?

• (a) Trading based on private insider information
• (b) Trading based on publicly available news reports
• (c) Trading based on patterns in past prices (technical analysis)
• (d) Trading based on a sophisticated statistical model of public data

Answer: (c)

Explanation: Weak-form efficiency means all information in past prices and trading volumes is already reflected in the current price. Therefore, technical analysis (trading on price patterns) should not be profitable. Strategies based on public information (b, d) would be unprofitable under semi-strong efficiency, and insider trading (a) under strong-form efficiency.

Question 3

A prediction market contract is priced at 0.70. Under the EMH, what does this mean?

• (a) The event will definitely occur
• (b) The event has a 70% probability of occurring, given all available information
• (c) 70% of traders think the event will occur
• (d) The expected payout is $0.70, but the true probability could be much higher or lower

Answer: (b)

Explanation: Under EMH, the price equals the market's best estimate of the probability, conditional on all available information. It is not a certainty (a), nor simply a headcount of beliefs (c). While (d) correctly states the expected payout is $0.70, the EMH further claims this is an unbiased estimate of the true probability, not just an arbitrary expected value.

Question 4

If prediction market prices follow a martingale, which statement is true?

• (a) Prices always increase over time
• (b) Prices never change
• (c) The expected value of tomorrow's price, given today's information, equals today's price
• (d) The variance of price changes is constant

Answer: (c)

Explanation: A martingale means $E[p_{t+1} | \mathcal{F}_t] = p_t$. This means price changes are unpredictable on average—the best forecast of tomorrow's price is today's price. Prices can and do change (ruling out (b)), and they need not always increase (ruling out (a)). Constant variance would describe a specific type of martingale but is not required (ruling out (d)).

Question 5

In the Wisdom of Crowds framework, which factor is MOST destructive to collective accuracy?

• (a) Individual errors that are large but independent
• (b) A small number of estimators
• (c) Correlated errors (lack of independence)
• (d) Slightly biased individual estimates

Answer: (c)

Explanation: Correlated errors are the most damaging because they create a floor on the crowd's error that cannot be reduced by adding more estimators. With correlation $\rho$, the crowd variance converges to $\rho\sigma^2$ as $N \to \infty$. Large independent errors (a) are reduced by $1/N$. A small number of estimators (b) is a quantitative limitation but not a fundamental one. Slight bias (d) is problematic but can sometimes be corrected.

Question 6

If 500 independent estimators each have estimation variance $\sigma^2 = 0.04$ and zero bias, what is the variance of their average?

• (a) 0.04
• (b) 0.008
• (c) 0.00008
• (d) 0.0004

Answer: (c)

Explanation: For independent estimators, $\text{Var}(\bar{\theta}) = \sigma^2 / N = 0.04 / 500 = 0.00008$.

Question 7

The Milgrom-Stokey No-Trade Theorem states that under ideal conditions, no trading should occur after private information arrives. Which assumption does prediction market trading MOST commonly violate to generate trade?

• (a) Agents are risk-averse
• (b) Agents have a common prior
• (c) The allocation is initially efficient
• (d) Information is private

Answer: (b)

Explanation: The most common departure from the No-Trade Theorem in prediction markets is heterogeneous priors—traders have genuinely different models of the world and different baseline beliefs. While risk aversion (a), initial allocation efficiency (c), and the nature of information (d) matter, the primary driver of trading in prediction markets is disagreement rooted in different priors.

Question 8

The Marginal Trader Hypothesis suggests that prediction market accuracy depends primarily on:

• (a) The average knowledge level of all traders
• (b) The total number of traders in the market
• (c) The activity and knowledge of the most informed traders who set the price
• (d) The market maker's algorithm

Answer: (c)

Explanation: The MTH states that market accuracy depends on the marginal traders—those whose trades actually move the price—not the average trader. Even if most traders are uninformed, a small fraction of informed, active traders can keep prices accurate by exploiting mispricings.

Question 9

In the Iowa Electronic Markets, research found that approximately what fraction of traders accounted for the majority of accurate price-setting?

• (a) About 50%
• (b) About 30%
• (c) About 10-15%
• (d) About 1%

Answer: (c)

Explanation: IEM research found that approximately 10-15% of traders were responsible for the majority of profitable trades and accurate price setting. These marginal traders traded more frequently, in larger amounts, and responded more quickly to new information.

Question 10

An information cascade occurs when:

• (a) Markets crash due to excessive selling
• (b) Individuals rationally ignore their private information and follow the actions of predecessors
• (c) Information is transmitted faster through social media than through markets
• (d) Multiple markets simultaneously incorporate the same news

Answer: (b)

Explanation: An information cascade occurs when the public history of actions (what previous people did) becomes so overwhelming that a rational agent should ignore their own private signal and copy the majority action. This can lead to collectively incorrect outcomes if early agents happened to have misleading signals.

Question 11

Why are prediction markets MORE resistant to information cascades than the standard sequential decision-making model?

• (a) Prediction market traders are smarter than average
• (b) Prediction markets use continuous prices that convey the strength of conviction, not just binary actions
• (c) Prediction markets are regulated to prevent herding
• (d) Prediction markets do not allow sequential trading

Answer: (b)

Explanation: In the standard cascade model, each person makes a binary decision (buy/don't buy), which discards information about conviction strength. In prediction markets, the continuous price mechanism allows traders to express how strongly they believe the event will occur, and the price encodes the cumulative conviction of all past traders. This richer information transmission makes cascades less likely.

Question 12

In an Agent-Based Model of a prediction market, zero-intelligence traders are agents that:

• (a) Always lose money
• (b) Submit orders at random prices within some range
• (c) Use artificial intelligence to optimize their trades
• (d) Have no effect on market dynamics

Answer: (b)

Explanation: Zero-intelligence traders, introduced by Gode and Sunder (1993), submit orders at random prices. They serve as a baseline for evaluating how much information aggregation comes from the market mechanism itself versus from informed agents. They do not necessarily always lose money (a), and they do affect market dynamics (d) by providing volume and noise.

Question 13

In the ABM framework, chartist (momentum) traders base their decisions on:

• (a) Their private estimate of the true probability
• (b) Recent price trends
• (c) Random noise
• (d) The fundamentals of the underlying event

Answer: (b)

Explanation: Chartists extrapolate from recent price movements. If prices have been rising, they buy; if falling, they sell. Their decision rule is based on past price trends, not on fundamental information about the event or random behavior.

Question 14

What happens to market accuracy in an ABM when the proportion of chartists becomes very large?

• (a) Accuracy improves because chartists add information
• (b) Accuracy stays the same because prices are determined by the market maker
• (c) Accuracy decreases and bubble-like behavior can emerge
• (d) All trading stops because chartists only follow trends

Answer: (c)

Explanation: When chartists dominate, momentum-driven trading can amplify small price deviations into large mispricings, creating bubble-like behavior. Chartists do not add fundamental information; they amplify trends, which can move prices away from the true probability.

Question 15

According to the Hanson-Oprea experimental results, what typically happens when someone attempts to manipulate a prediction market?

• (a) The market permanently moves in the direction the manipulator wants
• (b) The price temporarily moves, but informed traders correct it, and the manipulator loses money
• (c) The market shuts down to prevent manipulation
• (d) Other traders panic and the manipulation cascades

Answer: (b)

Explanation: Hanson and Oprea found that manipulation can temporarily move prices, but informed traders trade against the manipulation (profiting from the mispricing), which corrects the price. Manipulators lose money on average, effectively subsidizing information revelation by informed traders.

Question 16

What condition makes prediction markets MOST vulnerable to manipulation?

• (a) High liquidity with many informed traders
• (b) Low liquidity with few informed traders
• (c) Automated market makers with large liquidity parameters
• (d) Many active fundamentalist traders

Answer: (b)

Explanation: Markets are most vulnerable when liquidity is low (so a small trade can move the price significantly) and informed traders are few (so there is limited countervailing force to correct the manipulation). High liquidity (a), large market maker liquidity parameters (c), and many fundamentalist traders (d) all make manipulation harder.

Question 17

In a subsidized prediction market using an LMSR, the maximum loss to the market maker is:

• (a) Unlimited
• (b) $b \ln(n)$ where $b$ is the liquidity parameter and $n$ is the number of outcomes
• (c) Equal to the total trading volume
• (d) Zero, because the market maker always profits from the spread

Answer: (b)

Explanation: The LMSR has a bounded maximum loss of $b \ln(n)$. This is the worst-case subsidy the market sponsor must pay. The liquidity parameter $b$ controls both the depth of the market and the maximum loss.

Question 18

The Grossman-Stiglitz paradox states that:

• (a) Markets can be both efficient and inefficient at the same time
• (b) If markets were perfectly efficient, no one would have incentive to gather information, which means they cannot be perfectly efficient
• (c) Crowds always outperform experts
• (d) Information cascades are inevitable in all markets

Answer: (b)

Explanation: If prices perfectly reflected all information, there would be no profit opportunity from gathering costly information, so no one would gather information, and prices could not be perfectly informed. In equilibrium, markets must be slightly inefficient to provide incentives for information acquisition.

Question 19

Which of the following is an example of the favorite-longshot bias in prediction markets?

• (a) A contract priced at 0.50 that should be priced at 0.50
• (b) A contract priced at 0.10 for an event with true probability 0.05
• (c) A contract priced at 0.90 for an event with true probability 0.95
• (d) Both (b) and (c)

Answer: (d)

Explanation: The favorite-longshot bias means longshots (low probability events) are overpriced and favorites (high probability events) are underpriced. In (b), a 5% event is priced at 10% (overpriced longshot). In (c), a 95% event is priced at 90% (underpriced favorite). Both are examples of this bias.

Question 20

A prediction market contract is priced at 0.60 on Monday and drops to 0.40 after a major news event on Tuesday. Under semi-strong efficiency, what should happen?

• (a) The price should gradually drift from 0.60 to 0.40 over several days
• (b) The price should immediately jump to 0.40 when the news is released
• (c) The price should overshoot to 0.30 and then recover to 0.40
• (d) The price should not change because the news was already anticipated

Answer: (b)

Explanation: Semi-strong efficiency requires that prices fully and immediately incorporate all publicly available information. The adjustment should happen as a discrete jump when the news arrives, not as a gradual drift (a) or overshoot (c). If the news was not anticipated, the price should change; option (d) would only apply if the market had already priced in this possibility.

Question 21

Decision markets (conditional prediction markets) differ from standard prediction markets in that they:

• (a) Use real money instead of play money
• (b) Allow trading on what would happen conditional on different actions being taken
• (c) Are designed for decisions that have already been made
• (d) Require all traders to be experts in the relevant domain

Answer: (b)

Explanation: Decision markets create contracts conditional on different possible actions. For example: "What will unemployment be IF the government raises the minimum wage?" vs. "What will unemployment be IF it doesn't?" The key innovation is the conditional structure, which allows markets to inform decision-making by comparing expected outcomes under different policies.

Question 22

In the variance decomposition of crowd error, $\text{MSE} = \text{Bias}^2 + \text{Variance}$, adding more estimators primarily reduces:

• (a) The bias term
• (b) The variance term
• (c) Both equally
• (d) Neither; MSE is independent of crowd size

Answer: (b)

Explanation: Adding more estimators reduces the variance of the average (especially when errors are independent), but it does not reduce systematic bias. If every estimator has the same bias $\beta$, the average will also have bias $\beta$ regardless of crowd size. This is why diversity of perspective (which reduces both correlation and bias) is more valuable than simply adding more like-minded estimators.

Question 23

Which of the following real-world applications has provided the STRONGEST empirical evidence for information aggregation in prediction markets?

• (a) Sports betting markets
• (b) U.S. presidential election markets
• (c) Cryptocurrency price speculation
• (d) Internal corporate prediction markets

Answer: (b)

Explanation: U.S. presidential election markets (particularly the Iowa Electronic Markets, Intrade, and PredictIt) have been the most extensively studied and have provided the strongest empirical evidence. They have decades of data, well-defined outcomes for calibration testing, and a rich comparison set (polls, models, expert judgment). While sports betting (a) and corporate markets (d) also provide evidence, the election market literature is the most comprehensive.

Question 24

A prediction market designer wants to increase the speed of information aggregation. Which of the following changes would MOST likely help?

• (a) Increasing transaction fees
• (b) Reducing the minimum trade size and lowering fees
• (c) Adding a time delay between trades
• (d) Limiting trading to specific hours

Answer: (b)

Explanation: Reducing barriers to trading (smaller minimum trades, lower fees) makes it easier for informed traders to act on their information quickly, increasing the speed of information aggregation. Increasing fees (a), adding delays (c), and limiting trading hours (d) would all slow down information incorporation.

Question 25

Which statement BEST captures the overall lesson of information aggregation theory for prediction market practitioners?

• (a) Prediction markets always produce correct prices if enough people participate
• (b) Prediction markets aggregate information effectively under specific conditions (diversity, independence, sufficient liquidity, informed marginal traders) but can fail when these conditions are violated
• (c) The theoretical foundations of prediction markets are strong, but they never work well in practice
• (d) Information aggregation requires all traders to be rational and well-informed

Answer: (b)

Explanation: The central lesson of this chapter is that prediction markets are powerful but conditional information aggregation mechanisms. They work well when their conditions are met (diversity of opinion, independence of judgment, sufficient liquidity, the presence of informed marginal traders) and can fail when these conditions are violated (correlated beliefs, thin markets, absence of informed traders). They are neither infallible (a) nor impractical (c), and they do not require all traders to be informed (d)—just the marginal ones.

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