Quiz — Chapter 1: What Are Prediction Markets?
Test your understanding of the core concepts from Chapter 1. Try to answer each question before revealing the answer.
Scoring Guide
| Section | Points per Question | Total Points |
|---|---|---|
| Section 1: Multiple Choice (10) | 2 | 20 |
| Section 2: True/False (5) | 2 | 10 |
| Section 3: Fill in the Blank (3) | 3 | 9 |
| Section 4: Short Answer (4) | 5 | 20 |
| Section 5: Code Analysis (3) | 7 | 21 |
| Total | 80 |
| Score | Rating | Recommendation |
|---|---|---|
| 72–80 | Excellent | You are ready for Chapter 2 |
| 56–71 | Good | Review sections you missed, then proceed |
| 40–55 | Fair | Re-read the chapter with focus on weak areas |
| Below 40 | Needs work | Re-read the chapter carefully and redo exercises |
Section 1: Multiple Choice
Choose the single best answer for each question.
Q1. A binary prediction-market contract is trading at \$0.73. What is the market's implied probability that the event will occur?
(a) 27 % (b) 73 % (c) Cannot be determined without the No price (d) 50 %
Answer
**(b) 73 %** In a binary market, the Yes price directly represents the implied probability (assuming no overround or that the overround has been accounted for). A price of \$0.73 means the market assigns a 73 % probability to the event occurring. If there is an overround, you would need the No price to normalize, but in an ideal market, the answer is simply the price.Q2. Which of the following is NOT one of the conditions for the "wisdom of crowds" to function effectively?
(a) Diversity of opinion (b) Independence of judgment (c) Unanimous agreement among participants (d) Decentralization
Answer
**(c) Unanimous agreement among participants** The wisdom of crowds requires diversity, independence, and decentralization. Unanimous agreement is the *opposite* of what makes crowds wise — it suggests herding or groupthink, which destroys the diversity of opinion that allows errors to cancel out.Q3. In a prediction market, what role do noise traders serve?
(a) They provide accurate forecasts based on superior information (b) They manipulate the market to their advantage (c) They provide liquidity, making it possible for informed traders to trade (d) They serve no useful purpose and reduce market accuracy
Answer
**(c) They provide liquidity, making it possible for informed traders to trade** Noise traders may not have an information edge, but they are essential because they create the trading volume that allows informed traders to express their views. Without noise traders, informed traders would only trade with other informed traders, and the market would be illiquid.Q4. A categorical prediction market has contracts for four candidates: A (\$0.35), B (\$0.28), C (\$0.22), D (\$0.20). What is the overround?
(a) 0 % (b) 5 % (c) 10 % (d) 15 %
Answer
**(b) 5 %** The overround is calculated as the sum of all contract prices minus 1: $0.35 + 0.28 + 0.22 + 0.20 = 1.05$. The overround is $1.05 - 1.00 = 0.05 = 5\%$. This 5 % is the market maker's margin.Q5. Which type of prediction-market contract would you use to forecast the specific numerical value of next quarter's GDP growth?
(a) Binary contract (b) Categorical contract (c) Scalar (range) contract (d) Conditional contract
Answer
**(c) Scalar (range) contract** Scalar contracts are designed for numerical outcomes. They divide a continuous range into buckets (e.g., "0%–1%", "1%–2%", etc.), and the contract prices for each bucket form a probability distribution over the numerical range. You can calculate an expected value from this distribution.Q6. You believe an event has a 55 % chance of occurring. The Yes contract is trading at \$0.60. What is the expected value of buying one contract?
(a) +\$0.05 (b) -\$0.05 (c) +\$0.55 (d) -\$0.60
Answer
**(b) -\$0.05** Using the formula $\text{EV} = q - c = 0.55 - 0.60 = -0.05$. Since the contract price exceeds your probability estimate, this is a negative expected value trade. You should *not* buy.Q7. Which of the following is the strongest advantage of prediction markets over opinion polls?
(a) Prediction markets are cheaper to operate (b) Prediction markets have a larger sample size (c) Participants in prediction markets have a financial incentive for accuracy (d) Prediction markets are more widely trusted by the public
Answer
**(c) Participants in prediction markets have a financial incentive for accuracy** The key advantage is "skin in the game." When money is at stake, participants are motivated to research carefully, avoid wishful thinking, and update honestly. Poll respondents face no cost for being wrong.Q8. A prediction market has a total trading volume of \$3,000, 12 unique traders, and a bid-ask spread of \$0.08. What should your assessment of this market's price be?
(a) Highly reliable (b) Somewhat reliable (c) Skeptical — the market is thin (d) Impossible to assess without more information
Answer
**(c) Skeptical — the market is thin** All three indicators point to a thin (illiquid) market: volume below \$10,000, fewer than 50 traders, and a bid-ask spread wider than \$0.05. A thin market's price may not reflect broad consensus and is vulnerable to manipulation by a single trader.Q9. In the context of prediction markets, what does "resolution" mean?
(a) The market's trading volume reaching a threshold (b) The official determination of the contract's outcome (did the event happen or not) (c) The process of resolving disputes between traders (d) The market maker closing the market to new trades
Answer
**(b) The official determination of the contract's outcome (did the event happen or not)** Resolution is the process by which the market determines whether the event occurred and pays out accordingly. Well-defined resolution criteria — unambiguous, observable, and timely — are essential for a functional prediction market.Q10. A conditional prediction market contract is described as: "If Candidate X wins the presidency, what will the inflation rate be in 2026?" What happens to this contract if Candidate X loses?
(a) The contract resolves as "No" (b) The contract pays out based on the actual inflation rate regardless (c) The contract is voided and all money is returned (d) The contract remains open indefinitely
Answer
**(c) The contract is voided and all money is returned** In a conditional market, if the precondition (Candidate X wins) is not met, the contract does not resolve on the underlying question. Instead, it is voided (or "called off"), and participants receive their money back.Section 2: True or False
Determine whether each statement is true or false. Explain your reasoning.
Q11. "A prediction market price of \$0.80 guarantees that the event will happen."
Answer
**False.** A price of \$0.80 means the market assigns an 80 % probability to the event. This implies a 20 % chance the event does *not* happen — one in five. Probability estimates, no matter how high, do not constitute guarantees. Confusing probability with certainty is a common misunderstanding.Q12. "Prediction markets always outperform expert forecasters."
Answer
**False.** While prediction markets often outperform individual experts — especially for questions with diffuse information — they do not *always* do so. In domains where a small number of experts have deep, specialized knowledge (e.g., a specific technical question), a panel of genuine experts can outperform a prediction market, especially if the market has few participants.Q13. "The overround in a prediction market benefits the market maker at the expense of traders."
Answer
**True.** The overround (vig) is the margin built into the sum of contract prices exceeding \$1.00. It represents the cost of trading and goes to the market maker as compensation for providing liquidity. From the trader's perspective, the overround reduces expected returns.Q14. "If two platforms offer different prices on the same event, an arbitrage opportunity necessarily exists."
Answer
**False.** Different prices do not necessarily create an arbitrage opportunity. After accounting for transaction fees, withdrawal costs, overround, and the risk that the two platforms may use slightly different resolution criteria, the apparent price difference may not be exploitable. True arbitrage requires being able to simultaneously buy low and sell high on the *same* contract with the *same* resolution, net of all costs.Q15. "Play-money prediction markets (where no real money is at stake) can still produce reasonably accurate forecasts."
Answer
**True.** Empirical research has shown that play-money markets can be surprisingly accurate, though typically less so than real-money markets. Participants may still be motivated by reputation, competition, and intellectual engagement. However, the weaker financial incentive means play-money markets are more vulnerable to manipulation and less likely to attract serious effort from participants.Section 3: Fill in the Blank
Complete each statement with the correct term or formula.
Q16. The formula for removing the overround from a binary market and computing the implied probability of "Yes" is:
$P_{\text{implied}}(\text{Yes}) = \text{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$
Answer
$$P_{\text{implied}}(\text{Yes}) = \frac{p_Y}{p_Y + p_N}$$ where $p_Y$ is the Yes price and $p_N$ is the No price. Dividing by the sum of the two prices normalizes them so they add up to 1, effectively removing the market maker's overround.Q17. The expected value of buying a binary contract at price $c$ when you believe the probability of the event is $q$ is given by:
$\text{EV} = \text{\_\_\_\_\_\_\_\_\_\_\_}$
Answer
$$\text{EV} = q - c$$ This result follows from: $\text{EV} = q \times (1 - c) - (1 - q) \times c = q - qc - c + qc = q - c$. If $q > c$, the trade has positive expected value.Q18. The phenomenon where low-probability events tend to be overpriced in prediction markets and sports betting is known as the ____________ bias.
Answer
**Favorite-longshot bias** This well-documented bias means that "longshots" (low-probability outcomes) tend to be overpriced — traders pay more than the fair probability would justify — while "favorites" (high-probability outcomes) tend to be slightly underpriced.Section 4: Short Answer
Answer each question in 2–4 sentences.
Q19. Explain the concept of "information aggregation" in prediction markets. Why is it considered the primary mechanism that makes prediction markets accurate?
Answer
Information aggregation is the process by which a prediction market combines the private information of many individual traders into a single price. Each trader may hold only a partial view of reality — one person reads polls, another has an economic model, a third has on-the-ground intuition. When they trade, they push the price in the direction of their information, and the resulting equilibrium price reflects the sum total of all traders' knowledge. This is considered the primary mechanism because it means the market can "know" more than any individual participant.Q20. Why is liquidity important for the accuracy of a prediction market? What happens to price quality when liquidity is very low?
Answer
Liquidity determines how easily traders can buy or sell without significantly moving the price. In a liquid market, even large trades cause only small price movements, meaning the price is stable and reflects broad consensus. When liquidity is very low, a single trader's order can swing the price dramatically, the bid-ask spread widens, and the price may reflect the views of only a handful of participants rather than a genuine crowd. This makes the price unreliable as a probability estimate and more vulnerable to manipulation.Q21. Compare and contrast binary contracts and scalar contracts. When would you prefer one over the other?
Answer
A binary contract has exactly two outcomes (Yes or No) and pays \$1 if the event occurs. A scalar contract covers a continuous numerical range divided into buckets, forming a probability distribution. Binary contracts are simpler and more liquid, making them ideal for yes/no questions ("Will X happen?"). Scalar contracts are preferable when you care about *how much* rather than *whether* — for example, forecasting GDP growth, a stock price, or a temperature. Scalar contracts are more informationally rich but tend to be harder to make liquid because trading volume is split across many buckets.Q22. A skeptic argues that prediction markets can be easily manipulated by wealthy individuals. Explain the theoretical counter-argument and identify one real-world situation where the counter-argument may be insufficient.
Answer
The theoretical counter-argument is self-correction: if a wealthy individual pushes the price away from the true probability, they create a profit opportunity for informed traders who will bet against the manipulation, pushing the price back. The manipulator loses money in the process, making sustained manipulation costly. However, this counter-argument may be insufficient in low-liquidity markets where there are not enough informed traders to push back. The 2024 Polymarket presidential election markets illustrate this concern — large wallets ("whales") placed outsized bets, and whether this was manipulation or genuine information remains debated.Section 5: Code Analysis
Analyze the following Python code snippets.
Q23. What does the following function return when called with
implied_prob(0.55, 0.50)? Show your calculation.
def implied_prob(yes_price, no_price):
total = yes_price + no_price
return round(yes_price / total, 4)
Answer
**Returns: `0.5238`** Calculation: - `total = 0.55 + 0.50 = 1.05` - `yes_price / total = 0.55 / 1.05 = 0.52380952...` - `round(0.52380952, 4) = 0.5238` The function correctly computes the implied probability of "Yes" by normalizing the Yes price by the sum of both prices, removing the 5 % overround.Q24. The following code is supposed to calculate expected value but contains a bug. Identify the bug and provide the corrected version.
def expected_value(probability, price):
"""Calculate EV of buying a binary contract."""
profit_if_win = 1.0 - price
loss_if_lose = price
ev = probability * profit_if_win + (1 - probability) * loss_if_lose
return ev
Answer
**Bug:** The loss term should be *subtracted*, not *added*. When you lose, you lose your stake (the price you paid), which is a negative outcome. **Corrected version:**def expected_value(probability, price):
"""Calculate EV of buying a binary contract."""
profit_if_win = 1.0 - price
loss_if_lose = price
ev = probability * profit_if_win - (1 - probability) * loss_if_lose
return ev
Q25. Review the following code that generates a calibration check. What does it measure, and what would "good calibration" look like in the output?
import numpy as np
def calibration_check(prices, outcomes, n_bins=10):
"""
Check if market prices are well-calibrated.
Parameters
----------
prices : array-like
Market prices (implied probabilities) at market close.
outcomes : array-like
Actual outcomes (1 = event occurred, 0 = did not).
n_bins : int
Number of bins for grouping prices.
Returns
-------
dict
Bin midpoints and observed frequencies.
"""
prices = np.array(prices)
outcomes = np.array(outcomes)
bins = np.linspace(0, 1, n_bins + 1)
midpoints = []
observed_freqs = []
for i in range(n_bins):
mask = (prices >= bins[i]) & (prices < bins[i + 1])
if mask.sum() > 0:
midpoints.append((bins[i] + bins[i + 1]) / 2)
observed_freqs.append(outcomes[mask].mean())
return {"midpoints": midpoints, "observed_frequencies": observed_freqs}
Answer
**What it measures:** This function performs a *calibration analysis* on prediction market prices. It groups resolved contracts into bins by their closing price (implied probability), then calculates the fraction of contracts in each bin that actually resolved "Yes." **What "good calibration" looks like:** In a well-calibrated market, the observed frequency should closely match the bin midpoint. For example: - Contracts priced around 0.70 should resolve "Yes" about 70 % of the time. - Contracts priced around 0.30 should resolve "Yes" about 30 % of the time. If you plotted `midpoints` on the x-axis and `observed_frequencies` on the y-axis, good calibration would produce points close to the 45-degree diagonal line ($y = x$). Significant deviations from this line would indicate miscalibration — the market systematically over- or under-estimates probabilities in that range.End of Quiz — Chapter 1