"The best argument for prediction markets is not that they are perfect, but that they are less imperfect than the alternatives." — Justin Wolfers, economist and prediction-market researcher

Chapter 1 — What Are Prediction Markets?

Chapter Overview

Imagine it is late October 2024 and the United States presidential election is days away. Cable news pundits confidently contradict one another. Polling aggregators show a razor-thin race, with error bars that could flip the outcome. Your social-media feed is a firehose of certainty from both sides.

Now suppose someone tells you there is a single number — freely available, updating in real time — that synthesizes the beliefs of thousands of people who have put their own money on the line. That number is the price of a prediction-market contract. On Polymarket, one of the largest prediction platforms, the contract "Will the Republican nominee win the 2024 US presidential election?" traded between \$0.46 and \$0.67 in the final month alone, reflecting a live, incentive-compatible probability estimate that moved with every new piece of information the crowd absorbed.

This chapter is your entry point into that world. By the end you will be able to:

1. Explain what a prediction market is and why its prices encode probabilities.
2. Read a prediction-market price and immediately translate it to a forecast.
3. Write Python code that fetches real market data and computes implied probabilities.
4. Articulate when prediction markets outperform — and underperform — other forecasting tools.

Let's begin.

1.1 The Core Idea: Prices as Probabilities

1.1.1 A Simple Bet

Suppose your friend offers you a bet: "I'll pay you \$1 if it rains tomorrow; you pay me \$1 if it doesn't." Should you take it?

The answer depends on how likely you think rain is. If you believe rain is 70 % likely, the bet is worth taking — on average you expect to gain money. If you believe rain is only 30 % likely, the bet is a losing proposition.

A prediction market formalizes this kind of bet. It creates a contract that pays a fixed amount — typically \$1 — if and only if a specified event occurs. The market lets anyone buy or sell that contract at whatever price the crowd agrees on.

1.1.2 The Price-Probability Link

Here is the fundamental insight that makes prediction markets tick:

If a contract pays \$1 when event $E$ happens and \$0 otherwise, then the market price $p$ of that contract is the market's implied probability of $E$.

$$ p = P_{\text{market}}(E) $$

Why? Because of no-arbitrage reasoning. If the contract trades at \$0.65, a buyer is willing to risk \$0.65 to gain \$0.35 (for a total payout of \$1). That trade is profitable in expectation only if the buyer believes $P(E) > 0.65$. Conversely, a seller who receives \$0.65 now and must pay \$1 if $E$ occurs profits in expectation only if the seller believes $P(E) < 0.65$.

When the market clears — meaning buyers and sellers reach a price at which supply equals demand — the price is the consensus probability.

Intuition

Think of the price as a tug-of-war. Traders who believe the probability is higher than the current price buy contracts, pushing the price up. Traders who believe it is lower sell, pushing the price down. The equilibrium price balances these opposing forces and reflects the crowd's aggregate belief.

1.1.3 Worked Example: Reading a Prediction Market Price

On October 15, 2024, the Polymarket contract "Will the Democratic nominee win the 2024 US presidential election?" was trading at \$0.46.

What does that mean?

If you believed the true probability was 55 %, buying at \$0.46 would be a positive expected value trade (more on expected value in Section 1.6).

1.1.4 The Implied-Probability Formula

For a binary contract with a "Yes" price $p_Y$ and a "No" price $p_N$:

$$ P_{\text{implied}}(\text{Yes}) = \frac{p_Y}{p_Y + p_N} $$

In an ideal market with no fees, $p_Y + p_N = 1$, and the formula simplifies to $P_{\text{implied}} = p_Y$. In practice, market makers charge a spread (the overround or vig), so $p_Y + p_N > 1$. The formula above removes that overround to give a "fair" probability.

Example with overround:

$$ P_{\text{implied}}(\text{Yes}) = \frac{0.54}{1.04} \approx 0.519 = 51.9\% $$

$$ P_{\text{implied}}(\text{No}) = \frac{0.50}{1.04} \approx 0.481 = 48.1\% $$

The 4-cent overround (\$1.04 − \$1.00 = \$0.04) is the cost of trading; it compensates the market maker for providing liquidity.

Common Pitfall

Do not treat the raw contract price as the probability when an overround exists. Always normalize by dividing by the sum of complementary contract prices. Skipping this step systematically overstates probabilities.

1.2 Anatomy of a Prediction Market

A prediction market is more than just a price on a screen. Understanding the moving parts helps you reason about why a price is what it is and when you should trust it.

1.2.1 Participants

The interaction between informed and noise traders is essential. Noise traders provide liquidity — they make it possible for informed traders to express their views. Informed traders correct the price when it drifts from reality. Market makers sit in between, profiting from the spread while ensuring there is always someone to trade with.

1.2.2 Contract Types (Overview)

We will explore these in detail in Section 1.5. For now, note the four main families:

1. Binary (Yes/No): Pays \$1 if event happens, \$0 otherwise.
2. Categorical (Multi-outcome): A set of mutually exclusive contracts, one for each possible outcome (e.g., which party wins).
3. Scalar (Range): Pays based on where a numerical outcome falls within a range (e.g., GDP growth between 1 % and 5 %).
4. Conditional: Pays only if a precondition is met (e.g., "What will inflation be given that candidate X wins?").

1.2.3 Resolution

Every prediction-market contract specifies resolution criteria — the objective rules that determine whether the event occurred. Good resolution criteria are:

• Unambiguous: There must be no reasonable disagreement about the outcome.
• Observable: A trusted third party or data source settles the contract.
• Timely: The outcome is known within a bounded time window.

Ambiguous resolution criteria are one of the most common sources of disputes on prediction platforms.

1.2.4 The Information Aggregation Mechanism

The magic of a prediction market is information aggregation. Each trader brings a private signal — perhaps they saw a new poll, heard an insider rumor, or ran a statistical model. When they trade, they push the price toward their belief. The resulting price reflects the weighted average of all participants' information, where the weight is each trader's willingness to put money behind their view.

This is not just hand-waving. The theoretical result is known as the Efficient Markets Hypothesis (EMH) applied to prediction markets. Under certain conditions (enough traders, low transaction costs, no manipulation), the market price incorporates all available information at any point in time.

Real-World Application

The U.S. Intelligence Community explored prediction markets through the IARPA ACE (Aggregative Contingent Estimation) program. Researchers found that prediction markets consistently outperformed individual intelligence analysts in forecasting geopolitical events, precisely because they aggregated diverse information sources.

1.3 Why Prediction Markets Work

Prediction markets are not magic. They work because of several reinforcing mechanisms.

1.3.1 The Wisdom of Crowds

In 1906, Francis Galton observed that the median guess of 787 people at a county fair estimating the weight of an ox was within 1 % of the true weight — more accurate than any individual expert. This wisdom-of-crowds effect has been replicated across hundreds of studies: when you aggregate independent, diverse judgments, errors tend to cancel out, and what remains is a surprisingly accurate estimate.

Prediction markets are a structured mechanism for harnessing this effect.

Three conditions are necessary for crowd wisdom to work:

1. Diversity of opinion: Participants bring different information and models.
2. Independence: Judgments are not overly influenced by social pressure.
3. Decentralization: No single authority dictates the "right" answer.

Prediction markets satisfy all three — at least in principle. The monetary incentive discourages social conformity (condition 2), and anyone can participate (conditions 1 and 3).

1.3.2 Incentive Alignment: Skin in the Game

Polls and surveys ask people what they think will happen. Prediction markets ask people to bet on what will happen. The difference is profound.

When money is on the line, participants have an incentive to:

• Research carefully before trading.
• Update honestly when new information arrives.
• Avoid wishful thinking — your portfolio does not care about your political preferences.

Nassim Nicholas Taleb calls this "skin in the game." It aligns each trader's incentive with accuracy.

1.3.3 Continuous Updating

Unlike a poll that is conducted once a week, a prediction market updates continuously. Every trade shifts the price. A breaking news story can move the market within seconds. This gives prediction markets a temporal resolution that no other forecasting method can match.

1.3.4 Key Research Findings

The academic literature on prediction markets is extensive. Here are some highlights:

Best Practice

When citing prediction-market accuracy, always specify the liquidity and number of traders. A market with 5 participants and \$200 in total volume is not comparable to one with 5,000 participants and \$2 million in volume.

1.4 Real-World Examples

1.4.1 The 2024 US Presidential Election on Polymarket

Polymarket, a blockchain-based prediction platform, hosted the most heavily traded political prediction market of 2024. At its peak, the presidential-election contract had over \$1 billion in cumulative trading volume.

Key observations:

• Price trajectory: The contract hovered near \$0.50 (a toss-up) through the summer of 2024, then moved sharply after the September debate.
• Reaction to news: When President Biden withdrew from the race in July 2024, the Democratic-win contract jumped nearly 10 cents within an hour.
• Divergence from polls: In October 2024, Polymarket priced the Republican nominee at roughly \$0.60 while polling averages showed a near-tie. This divergence sparked debate about whether the market was biased by large traders or whether it was incorporating information that polls missed.
• Resolution: The contract resolved on Election Day, November 5, 2024, based on the Associated Press call.

This case illustrates both the power and the limitations of prediction markets. The market incorporated information quickly, but it also raised questions about whale effects — a small number of very large traders disproportionately moving the price.

1.4.2 COVID-19 Timeline Markets

During the pandemic, platforms such as Metaculus and Good Judgment Open hosted markets on questions like:

• "When will 100 million Americans be vaccinated?"
• "Will the WHO declare the pandemic over by December 2023?"
• "Will a new variant of concern emerge by Q1 2022?"

These markets provided decision-makers with continuously updated probability estimates at a time when expert opinions were unusually divergent. Post-hoc calibration analyses showed that the market-implied probabilities were well-calibrated overall, although they underestimated tail risks (very unlikely events that did occur).

1.4.3 Sports Betting: The Original Prediction Market

Before Polymarket, before the Iowa Electronic Markets, there were bookmakers. Sports betting is, structurally, a prediction market. A betting line of −150 on a team implies a certain win probability (approximately 60 %).

Sports betting markets are among the most liquid prediction markets in the world, and they are remarkably efficient. Academic studies have shown that closing betting lines are approximately as accurate as sophisticated statistical models.

Intuition

If you can understand a sports betting line, you already understand prediction markets. The only difference is that prediction markets extend the concept from sports to everything — politics, science, business, weather, and more.

1.4.4 Corporate Prediction Markets

Several large companies have run internal prediction markets:

• Google: Ran markets for over a decade, letting employees bet on product-launch dates, quarterly targets, and strategic decisions. Bo Cowgill's research showed these markets outperformed official forecasts.
• Hewlett-Packard: Pioneered corporate prediction markets in the late 1990s for printer-sales forecasting. Internal markets beat official HP sales forecasts in 6 out of 8 quarters studied.
• Microsoft: Used prediction markets to estimate software-release timelines and bug counts.
• Ford Motor Company: Experimented with markets for vehicle-sales forecasts.

Corporate prediction markets face unique challenges: small participant pools, employees gaming the system, and management resistance to unflattering forecasts.

1.4.5 Weather Derivatives

Weather derivatives are financial contracts whose value depends on weather outcomes — temperature, rainfall, snowfall. While technically derivatives rather than pure prediction markets, they function the same way: the price embeds the market's consensus forecast for the weather variable.

Energy companies use weather derivatives to hedge against warm winters (which reduce heating-fuel demand) or cool summers (which reduce air-conditioning load). The Chicago Mercantile Exchange (CME) lists standardized weather contracts for dozens of cities.

1.5 Types of Prediction Markets

1.5.1 Binary (Yes/No) Markets

A binary market has exactly two outcomes: the event happens or it does not.

Example: "Will the Federal Reserve cut interest rates at its March 2025 meeting?"

• Yes contract pays \$1 if rates are cut, \$0 otherwise.
• No contract pays \$1 if rates are *not* cut, \$0 otherwise.

Since exactly one of the two outcomes must occur:

$$ p_{\text{Yes}} + p_{\text{No}} = 1 \quad (\text{in a frictionless market}) $$

Binary markets are the simplest and most common type. Most examples in this book use binary contracts unless stated otherwise.

1.5.2 Categorical (Multi-Outcome) Markets

A categorical market covers an event with $k > 2$ mutually exclusive and collectively exhaustive outcomes.

Example: "Who will win the 2024 FIFA Ballon d'Or?" Contracts might exist for Rodri, Vinicius Jr., Bellingham, and an "Other" bucket.

For $k$ outcomes:

$$ \sum_{i=1}^{k} p_i = 1 \quad (\text{in a frictionless market}) $$

Each contract's price is the implied probability of that outcome. If Rodri trades at \$0.35, the market believes he has a 35 % chance of winning.

1.5.3 Scalar (Range) Markets

Scalar markets forecast a numerical value rather than a discrete outcome.

Example: "What will US GDP growth be in Q4 2025?"

A common implementation divides the range into buckets:

These prices form a probability distribution over the numerical range. You can compute the market's expected value, variance, and other moments from this distribution.

The expected value from a scalar market:

$$ E[X] = \sum_{i=1}^{k} p_i \cdot m_i $$

where $m_i$ is the midpoint of bucket $i$ and $p_i$ is the contract price (normalized to sum to 1).

Using the example above:

$$ E[\text{GDP growth}] = 0.05 \times (-0.5\%) + 0.15 \times 0.5\% + 0.35 \times 1.5\% + 0.30 \times 2.5\% + 0.10 \times 3.5\% + 0.05 \times 4.5\% $$

$$ = -0.025\% + 0.075\% + 0.525\% + 0.750\% + 0.350\% + 0.225\% = 1.90\% $$

The market's consensus GDP-growth forecast is 1.90 %.

1.5.4 Conditional Markets

Conditional markets answer "if-then" questions.

Example: "If the Republican nominee wins the presidency, what will the S&P 500 return in 2025?"

A conditional market only activates (or only resolves) if the precondition is met. If the Republican nominee loses, the contract is voided and all participants get their money back.

Conditional markets are powerful because they let you isolate the causal or informational relationship between two variables. They are also rare and hard to make liquid, because the precondition reduces the effective market size.

$$ P(A \mid B) = \frac{\text{Price of conditional contract "A given B"}}{\text{Price of contract "B"}} $$

Real-World Application

Robin Hanson, the economist who coined the term "futarchy," proposed governing societies by conditional prediction markets: enact a policy if and only if a conditional prediction market says that policy will achieve a specified goal. While futarchy remains theoretical, it illustrates the power of conditional markets.

1.6 Your First Prediction Market Analysis in Python

Let's turn theory into code. In this section we will:

1. Create synthetic but realistic market data.
2. Convert prices to implied probabilities.
3. Calculate expected value for a hypothetical trade.
4. Visualize a price time series.

1.6.1 Setting Up

We will use standard Python libraries. If you do not have them installed:

pip install matplotlib numpy pandas

1.6.2 Converting Prices to Probabilities

def implied_probability(yes_price: float, no_price: float) -> tuple[float, float]:
    """
    Convert prediction-market contract prices to implied probabilities
    by removing the overround.

    Parameters
    ----------
    yes_price : float
        Current market price of the "Yes" contract (0-1 scale).
    no_price : float
        Current market price of the "No" contract (0-1 scale).

    Returns
    -------
    tuple[float, float]
        (probability_yes, probability_no), each in [0, 1].
    """
    total = yes_price + no_price
    prob_yes = yes_price / total
    prob_no = no_price / total
    return prob_yes, prob_no


# Example
yes_price = 0.54
no_price = 0.50

prob_yes, prob_no = implied_probability(yes_price, no_price)
print(f"Yes price: ${yes_price:.2f}  -> Implied P(Yes) = {prob_yes:.1%}")
print(f"No  price: ${no_price:.2f}  -> Implied P(No)  = {prob_no:.1%}")
print(f"Overround: {yes_price + no_price - 1:.2%}")

Output:

Yes price: $0.54  -> Implied P(Yes) = 51.9%
No  price: $0.50  -> Implied P(No)  = 48.1%
Overround: 4.00%

1.6.3 Calculating Expected Value

Expected value (EV) is the average profit or loss you would experience if you made the same trade many times.

$$ \text{EV} = P(\text{win}) \times \text{profit if win} - P(\text{lose}) \times \text{loss if lose} $$

For a binary contract purchased at price $c$ with your personal probability estimate $q$:

$$ \text{EV} = q \times (1 - c) - (1 - q) \times c = q - c $$

This elegant result says: your expected value is simply your probability minus the cost.

def expected_value(your_probability: float, contract_price: float) -> float:
    """
    Calculate the expected value of buying a binary prediction-market contract.

    Parameters
    ----------
    your_probability : float
        Your personal estimate of the event probability (0-1).
    contract_price : float
        The current market price of the contract (0-1).

    Returns
    -------
    float
        Expected profit per contract.  Positive = profitable trade.
    """
    return your_probability - contract_price


# Example: you believe there is a 60% chance the event happens, contract costs $0.52
my_prob = 0.60
price = 0.52
ev = expected_value(my_prob, price)
print(f"Your probability: {my_prob:.0%}")
print(f"Contract price:   ${price:.2f}")
print(f"Expected value:   ${ev:.2f} per contract")
print(f"Verdict:          {'BUY' if ev > 0 else 'PASS'}")

Output:

Your probability: 60%
Contract price:   $0.52
Expected value:   $0.08 per contract
Verdict:          BUY

Intuition

The expected-value formula $\text{EV} = q - c$ is so simple it almost feels wrong. But it captures the full story: you pay $c$ for a contract that pays \$1 with your estimated probability $q$. If $q > c$, the trade has positive EV.

1.6.4 Visualizing a Price Time Series

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

def generate_synthetic_market_data(
    start_price: float = 0.50,
    n_days: int = 90,
    volatility: float = 0.02,
    seed: int = 42,
) -> pd.DataFrame:
    """
    Generate synthetic daily prediction-market data using a bounded random walk.

    Parameters
    ----------
    start_price : float
        Opening price on day 0.
    n_days : int
        Number of trading days.
    volatility : float
        Daily price standard deviation.
    seed : int
        Random seed for reproducibility.

    Returns
    -------
    pd.DataFrame
        Columns: date, price, volume.
    """
    rng = np.random.default_rng(seed)
    prices = [start_price]
    for _ in range(n_days - 1):
        change = rng.normal(0, volatility)
        new_price = np.clip(prices[-1] + change, 0.01, 0.99)
        prices.append(round(new_price, 4))

    dates = pd.date_range("2024-08-01", periods=n_days, freq="D")
    volumes = rng.integers(50_000, 500_000, size=n_days)

    return pd.DataFrame({"date": dates, "price": prices, "volume": volumes})


# Generate and plot
df = generate_synthetic_market_data(start_price=0.48, n_days=90)

fig, ax1 = plt.subplots(figsize=(12, 5))
ax1.plot(df["date"], df["price"], color="steelblue", linewidth=1.5)
ax1.set_ylabel("Contract Price ($)", fontsize=12)
ax1.set_xlabel("Date", fontsize=12)
ax1.set_title("Synthetic Prediction Market: Daily Contract Price", fontsize=14)
ax1.axhline(y=0.50, color="gray", linestyle="--", alpha=0.5, label="50% line")
ax1.set_ylim(0, 1)
ax1.legend()

# Add volume bars on secondary axis
ax2 = ax1.twinx()
ax2.bar(df["date"], df["volume"], alpha=0.15, color="orange", label="Volume")
ax2.set_ylabel("Daily Volume ($)", fontsize=12)

fig.tight_layout()
plt.savefig("market_price_timeseries.png", dpi=150)
plt.show()

This script produces a chart with the contract price plotted as a line and trading volume shown as translucent orange bars. You will see the price meander around 0.50, occasionally drifting higher or lower as our synthetic random walk simulates incoming information.

Common Pitfall

When visualizing prediction-market prices, always set the y-axis to [0, 1]. Prices are bounded by design, and using auto-scaling can make small movements look dramatic, misleading the viewer.

1.7 Prediction Markets vs. Other Forecasting Methods

No forecasting method is universally best. The right tool depends on the question, the available data, and the stakes. Here is how prediction markets stack up.

1.7.1 Comparison Table

1.7.2 When Prediction Markets Shine

• Fast-moving events: Elections, policy announcements, breaking news.
• Questions with diffuse information: No single expert has the full picture.
• Continuous monitoring: You need a probability that updates in real time.
• Hard-to-model questions: "Will this startup succeed?" is hard to model statistically but easy to form a market around.

1.7.3 When Other Methods Are Better

• Stable, data-rich environments: Statistical models can outperform markets when the underlying process is well-understood and data is abundant (e.g., weather forecasting over a 3-day horizon).
• Private or classified information: You cannot have a public market on military secrets.
• Small populations: A prediction market with 10 traders is unlikely to beat a panel of 3 genuine experts.
• Ethical constraints: Creating a market on someone's death or a terrorist attack raises moral objections (see the DARPA FutureMAP controversy).

Best Practice

Combine methods. The best forecasting ensembles typically merge statistical models, expert judgment, and prediction-market signals. Prediction markets are a complement, not a replacement.

1.8 Practical Considerations

1.8.1 Liquidity and Thin Markets

A market's accuracy depends on its liquidity — the amount of money available for trading. In a thin market (few traders, low volume), a single large order can swing the price dramatically, and the price may not reflect broad consensus.

Rule of thumb: Be skeptical of prediction-market prices when:

• Total volume is below \$10,000.
• Fewer than 50 unique traders have participated.
• The bid-ask spread is wider than 5 cents.

1.8.2 Market Manipulation

Can someone with deep pockets manipulate a prediction market? In theory, manipulation is self-correcting: if a whale pushes the price away from the true probability, informed traders can profit by trading against the whale, pushing the price back.

In practice, manipulation is a real concern in low-liquidity markets. The 2024 Polymarket election markets saw accusations of manipulation when a few large wallets placed outsized bets. Whether those trades were manipulation or genuine information is still debated.

Key question: Is the market liquid enough that manipulation is costly?

1.8.3 Regulatory Status

Prediction markets exist in a regulatory gray area in many countries:

In 2023, a federal appeals court ruled that Kalshi could offer Congressional-control contracts over the CFTC's objections, a landmark decision for the industry. The regulatory landscape is evolving rapidly.

1.8.4 Other Limitations

• Subsidized vs. real-money markets: Play-money markets (e.g., early Metaculus) may be less accurate because participants have weaker incentives.
• Resolution risk: Ambiguous resolution criteria can distort prices as traders price in the probability of a resolution dispute rather than the event itself.
• Long-horizon markets: Markets on events years in the future tend to be illiquid because capital is tied up for extended periods.
• Favorite-longshot bias: Across many markets, low-probability events tend to be overpriced (people overpay for longshots). This is a well-documented bias in sports betting and prediction markets alike.

Common Pitfall

Do not confuse "the market price is 80 %" with "the event will definitely happen." An 80 % probability means the event does not happen one time in five. Respecting uncertainty is central to good forecasting.

1.9 Chapter Summary

Key Concepts

1. Prediction markets are exchange-traded contracts that pay out based on the outcome of future events.
2. The market price of a binary contract is the crowd's implied probability of the event.
3. Prediction markets work because of information aggregation, incentive alignment, and the wisdom of crowds.
4. There are four main contract types: binary, categorical, scalar, and conditional.
5. Prediction markets update continuously and are well-calibrated in liquid markets.
6. Liquidity, manipulation, and regulation are the main practical concerns.

Key Formulas

Decision Framework

When encountering a prediction-market price, ask yourself:

1. Is the market liquid? (Volume > \$10k, 50+ traders, tight spread)
2. Are resolution criteria clear? (Unambiguous, observable, timely)
3. Is there an overround? (Normalize prices if so)
4. Do I have an information edge? (If EV > 0 and I trust my estimate, consider trading)
5. How does this compare with other forecasts? (Polls, models, experts)

What's Next

In Chapter 2: A Brief History of Prediction Markets, we trace the fascinating evolution of prediction markets from ancient origins to modern platforms. You will learn:

• How prediction markets emerged from early betting pools and election wagers.
• The key academic breakthroughs that established the theoretical foundations.
• How modern platforms like Polymarket, Kalshi, and Metaculus carry forward centuries of innovation.
• Why understanding this history helps you navigate today's market landscape.

Understanding the history of prediction markets gives essential context — nearly every design choice in today's platforms reflects lessons learned over centuries of experimentation with collective forecasting.

End of Chapter 1