Quiz: The Frontier — Research Directions
Test your understanding of frontier research directions in prediction markets. Each question has a single best answer. Expand the answer sections to check your work.
Question 1
What is the primary advantage of using LLMs as forecasters compared to human forecasters?
A) LLMs are always more accurate than humans B) LLMs can process vast amounts of text and scale to thousands of questions simultaneously C) LLMs have no cognitive biases D) LLMs can access real-time information better than humans
Answer
**B) LLMs can process vast amounts of text and scale to thousands of questions simultaneously.** LLMs are not always more accurate than expert humans, and they do exhibit systematic biases (anchoring on training data, sycophancy, sensitivity to prompt framing). Their key advantage is scalability: a single LLM can produce forecasts for thousands of questions at minimal marginal cost, whereas human forecasters are expensive and scarce.Question 2
Which prompting strategy is designed to counteract the anchoring bias in LLM forecasts?
A) Chain-of-thought prompting B) Base rate prompting C) Adversarial prompting D) Decomposition prompting
Answer
**B) Base rate prompting.** Base rate prompting explicitly asks the LLM to identify and consider the relevant base rate before making a prediction. This counteracts anchoring by forcing the model to start from a statistical baseline rather than an intuitive anchor. Adversarial prompting challenges overconfidence, while decomposition breaks the question into sub-questions.Question 3
In the context of AI-augmented prediction market trading, what does a "signal extraction layer" do?
A) Filters out market noise to produce cleaner price data B) Extracts private trading signals from other participants' orders C) Processes news, social media, and data feeds to generate probability estimates D) Encrypts trading signals for privacy
Answer
**C) Processes news, social media, and data feeds to generate probability estimates.** The signal extraction layer is the component of an AI trading system that ingests unstructured data (news articles, social media posts, economic data releases) and converts it into structured probability estimates or trading signals. This layer is distinct from the strategy layer (which decides what to trade) and the execution layer (which submits orders).Question 4
What mathematical property must a cost function $C(\mathbf{q})$ satisfy for a valid automated market maker?
A) $C$ must be linear B) $C$ must be concave C) $C$ must be convex and differentiable, with $\sum_i \partial C / \partial q_i = 1$ D) $C$ must be bounded above
Answer
**C) $C$ must be convex and differentiable, with $\sum_i \partial C / \partial q_i = 1$.** Convexity ensures that the market maker's worst-case loss is bounded. Differentiability ensures that prices are well-defined (prices are the partial derivatives). The constraint that partial derivatives sum to 1 ensures that prices form a valid probability distribution. The LMSR satisfies all these properties.Question 5
A zero-knowledge proof in a prediction market context allows a trader to:
A) Prove they made a profitable trade without revealing their identity B) Prove they have sufficient balance to trade without revealing their actual balance C) Prove they know the outcome of an event without revealing what it is D) Prove they are human without completing a CAPTCHA
Answer
**B) Prove they have sufficient balance to trade without revealing their actual balance.** A ZKP allows a prover to convince a verifier that a statement is true without revealing any information beyond the truth of the statement. In prediction markets, a key application is proving sufficient balance for a trade (the statement: "my balance >= trade cost") without revealing the actual balance (the witness).Question 6
What is the relationship between the privacy parameter $\epsilon$ in differential privacy and the amount of noise added?
A) Higher $\epsilon$ means more noise and stronger privacy B) Higher $\epsilon$ means less noise and weaker privacy C) $\epsilon$ and noise are unrelated D) Higher $\epsilon$ means the same noise but applied less frequently
Answer
**B) Higher $\epsilon$ means less noise and weaker privacy.** In differential privacy, $\epsilon$ controls the privacy-utility tradeoff. For the Laplace mechanism, noise is drawn from $\text{Lap}(\Delta f / \epsilon)$, where $\Delta f$ is the sensitivity. As $\epsilon$ increases, the noise scale decreases, providing less privacy protection but better utility (more accurate published statistics).Question 7
In the Bayesian Truth Serum (BTS) mechanism, agents are rewarded based on:
A) The accuracy of their predictions compared to the eventual outcome B) How closely their reports match the majority vote C) A combination of their report's "surprisingly common" frequency and their prediction of others' reports D) The amount of money they stake on their report
Answer
**C) A combination of their report's "surprisingly common" frequency and their prediction of others' reports.** BTS scores agents based on two components: (1) an information score that rewards reports that are "surprisingly common" — more frequent than predicted by others' meta-predictions, and (2) a prediction score that rewards accurate predictions of the distribution of others' reports. This mechanism incentivizes truthful reporting even without access to ground truth.Question 8
What is the key advantage of Shamir's Secret Sharing for multi-party computation in prediction markets?
A) It is computationally efficient enough for real-time trading B) It allows a secret to be split among $n$ parties such that any $k$ can reconstruct it, but fewer than $k$ learn nothing C) It provides both encryption and authentication D) It eliminates the need for a trusted third party entirely
Answer
**B) It allows a secret to be split among $n$ parties such that any $k$ can reconstruct it, but fewer than $k$ learn nothing.** Shamir's $(k, n)$ secret sharing scheme uses polynomial interpolation to split a secret among $n$ parties with a threshold of $k$. This is useful for prediction markets because trade data can be split among multiple servers, and the market can function as long as $k$ servers cooperate, while no subset smaller than $k$ can learn individual trading positions.Question 9
Homomorphic encryption allows:
A) Encryption that gets stronger over time B) Computation on encrypted data without decrypting it first C) Encryption that works on both text and numbers D) Simultaneous encryption and compression
Answer
**B) Computation on encrypted data without decrypting it first.** Homomorphic encryption enables operations on ciphertexts that produce encrypted results which, when decrypted, match the result of performing corresponding operations on the plaintexts. For prediction markets, this means an operator could compute aggregate statistics (e.g., average price) on encrypted trades without ever seeing individual positions.Question 10
What is the "oracle problem" in decentralized prediction markets?
A) The difficulty of finding questions that are interesting to trade B) The challenge of determining who resolves market outcomes truthfully in a trustless system C) The computational cost of running prediction markets on blockchain D) The problem of low liquidity in decentralized markets
Answer
**B) The challenge of determining who resolves market outcomes truthfully in a trustless system.** The oracle problem is fundamental to decentralized prediction markets: someone (or some mechanism) must determine whether an event occurred and report the outcome to the smart contract. In a trustless system, any single oracle can be bribed or mistaken. Solutions include multi-oracle systems (e.g., UMA's DVM, Kleros), Schelling point mechanisms, and reputation staking.Question 11
In the context of peer prediction, what does "strictly proper" mean for a scoring rule?
A) The scoring rule always produces positive scores B) Truthful reporting uniquely maximizes the expected score C) The scoring rule is fair to all participants D) The scoring rule can be computed in polynomial time
Answer
**B) Truthful reporting uniquely maximizes the expected score.** A scoring rule is strictly proper if an agent's expected score is uniquely maximized by reporting their true belief. This is the key property needed for incentive compatibility in peer prediction: if the mechanism uses a strictly proper scoring rule, rational agents have no incentive to misreport. The Brier score and logarithmic scoring rule are both strictly proper.Question 12
What is the primary challenge of using prediction markets for causal (interventional) questions?
A) Causal questions are too complex for participants to understand B) The counterfactual world cannot be directly observed, making settlement difficult C) Causal inference requires controlled experiments that markets cannot conduct D) Causal markets always attract manipulators
Answer
**B) The counterfactual world cannot be directly observed, making settlement difficult.** For a causal market (e.g., "What would unemployment be if the minimum wage increased by 20%?"), the outcome depends on a specific intervention. If the intervention does not occur, we cannot observe the counterfactual and cannot settle the market. Decision markets partially address this by conditioning on the decision-maker's choice, but the fundamental counterfactual problem remains.Question 13
Advanced composition in differential privacy improves on basic composition by:
A) Allowing unlimited queries with bounded privacy loss B) Showing that privacy loss grows as $O(\sqrt{k} \cdot \epsilon)$ rather than $O(k \cdot \epsilon)$ for $k$ queries C) Eliminating the need for noise entirely after enough queries D) Providing exact rather than approximate privacy guarantees
Answer
**B) Showing that privacy loss grows as $O(\sqrt{k} \cdot \epsilon)$ rather than $O(k \cdot \epsilon)$ for $k$ queries.** Basic composition says that $k$ applications of an $\epsilon$-DP mechanism result in $k\epsilon$-DP overall. Advanced composition shows that for $(\epsilon, \delta)$-DP, the total privacy loss after $k$ queries is approximately $\sqrt{2k \ln(1/\delta')} \cdot \epsilon + k\epsilon(e^\epsilon - 1)$, which grows as $O(\sqrt{k})$ rather than $O(k)$. This is critical for prediction markets that publish many rounds of price updates.Question 14
What is the "sycophancy" bias in LLM forecasting?
A) The tendency to produce overly complex forecasts B) The tendency to agree with or tell the user what they want to hear C) The tendency to favor forecasts from authoritative sources D) The tendency to produce round-number probabilities
Answer
**B) The tendency to agree with or tell the user what they want to hear.** Sycophancy is a well-documented LLM behavior where the model adjusts its outputs to align with perceived user preferences or expectations. In forecasting, this manifests as the LLM shifting its probability estimate based on framing cues in the prompt (e.g., an optimistic prompt leads to higher probabilities). This bias must be actively mitigated through careful prompt design.Question 15
In cross-chain prediction market arbitrage, the minimum profitable price divergence must exceed:
A) The gas fees on both chains B) The sum of trading fees on both chains plus bridge fees and slippage C) The block time difference between the two chains D) The oracle fee for price verification
Answer
**B) The sum of trading fees on both chains plus bridge fees and slippage.** Cross-chain arbitrage requires buying on the cheaper chain and selling on the more expensive chain. The profit must exceed all transaction costs: trading fees on Chain A, trading fees on Chain B, bridge fees for moving assets between chains, and any slippage from the trades themselves. Bridge latency also introduces risk that prices may change before the arbitrage completes.Question 16
What is the key insight of the "wisdom of crowds" effect that applies to both human and AI forecaster aggregation?
A) Crowds are always smarter than individuals B) Errors of diverse, independent forecasters tend to cancel out when aggregated C) Larger crowds always produce better forecasts D) Crowd aggregation eliminates all systematic biases
Answer
**B) Errors of diverse, independent forecasters tend to cancel out when aggregated.** The wisdom of crowds depends on two conditions: diversity (forecasters use different information and methods) and independence (their errors are not correlated). When these conditions hold, random errors cancel out in the aggregate, leaving a more accurate consensus. This applies to both human forecaster pools and ensembles of AI models. Crowds can still be systematically wrong if all members share the same bias.Question 17
A Pedersen commitment $C = g^v h^r \bmod p$ provides which two properties?
A) Confidentiality and integrity B) Hiding (the commitment reveals nothing about $v$) and binding (the committer cannot change $v$) C) Authentication and non-repudiation D) Forward secrecy and backward secrecy
Answer
**B) Hiding (the commitment reveals nothing about $v$) and binding (the committer cannot change $v$).** The Pedersen commitment has two cryptographic properties. Hiding: given $C$, an observer cannot determine $v$ because the random blinding factor $r$ masks it (computationally hiding under the discrete log assumption). Binding: the committer cannot find a different $(v', r')$ that produces the same $C$ (computationally binding under the discrete log assumption). This makes it useful for sealed-bid trading in prediction markets.Question 18
What is the main limitation of using reinforcement learning for prediction market trading?
A) RL algorithms are too slow to execute trades B) The non-stationary environment and sparse rewards make training difficult C) RL cannot handle continuous action spaces D) RL requires real-money markets to learn effectively
Answer
**B) The non-stationary environment and sparse rewards make training difficult.** Prediction market environments are challenging for RL because: (1) the state space is non-stationary — the information environment and other traders' strategies evolve over time; (2) rewards are sparse — a binary market only pays off at resolution, which may be months away; (3) the environment is partially observable — other traders' beliefs and positions are hidden. These challenges require specialized RL techniques like reward shaping and curriculum learning.Question 19
In a decision market, why does the "strategic trader" problem arise?
A) Traders may manipulate prices to influence the decision-maker's choice in their favor B) Traders have imperfect information about the decision C) The decision-maker may ignore market prices D) Transaction costs make small trades unprofitable
Answer
**A) Traders may manipulate prices to influence the decision-maker's choice in their favor.** In a decision market, the decision-maker commits to choosing the policy with the higher market price. This creates an incentive for traders who prefer a particular policy (for reasons unrelated to its effectiveness) to buy shares in that policy's market, pushing the price up and potentially causing the decision-maker to choose the "wrong" policy. This is a fundamental game-theoretic challenge for decision markets.Question 20
What is "automated mechanism design" in the context of prediction markets?
A) Using AI to detect market manipulation B) Automatically matching buyers and sellers C) Using optimization algorithms to find market mechanisms with optimal properties (accuracy, cost, incentive compatibility) D) Designing markets that run without human intervention
Answer
**C) Using optimization algorithms to find market mechanisms with optimal properties (accuracy, cost, incentive compatibility).** Automated mechanism design uses computational optimization to search over a parameterized family of market mechanisms (e.g., different cost functions, fee structures, liquidity parameters) to find the mechanism that optimizes a specified objective (e.g., forecast accuracy, bounded market maker loss, incentive compatibility). This contrasts with hand-designed mechanisms like LMSR.Question 21
The "privacy-utility tradeoff" in differential privacy for prediction markets fundamentally means:
A) More participants lead to better privacy but worse accuracy B) Stronger privacy guarantees require more noise, which degrades forecast accuracy C) Private markets attract fewer participants D) Privacy and utility are independent dimensions
Answer
**B) Stronger privacy guarantees require more noise, which degrades forecast accuracy.** The privacy-utility tradeoff is fundamental to differential privacy. To protect individual traders' privacy, noise must be added to published statistics (prices, volumes). More noise (smaller $\epsilon$) provides stronger privacy but makes the published prices less accurate. The key question is whether there exists an $\epsilon$ value that provides meaningful privacy while preserving useful price signals. For large markets, the answer is typically yes.Question 22
Which of the following is NOT an open problem in prediction market research (as of 2025)?
A) Designing manipulation-resistant oracle mechanisms B) Achieving incentive-compatible aggregation with privacy C) Computing the equilibrium price in a binary prediction market with LMSR D) Long-horizon forecasting with meaningful incentives
Answer
**C) Computing the equilibrium price in a binary prediction market with LMSR.** Computing prices in a binary LMSR market is straightforward — it is simply $e^{q_i/b} / \sum_j e^{q_j/b}$, which is computationally trivial. The other three are genuine open problems: oracle manipulation resistance, privacy-compatible incentive design, and long-horizon incentive structures remain active research areas with no fully satisfactory solutions.Question 23
Why is the geometric mean preferred over the arithmetic mean for aggregating LLM probability forecasts from multiple prompting strategies?
A) The geometric mean is always closer to 0.5 B) The geometric mean handles extreme probabilities better and is equivalent to averaging log-odds C) The geometric mean is computationally cheaper D) The geometric mean produces probabilities that are always between 0 and 1
Answer
**B) The geometric mean handles extreme probabilities better and is equivalent to averaging log-odds.** The geometric mean of probabilities, after normalization, is equivalent to averaging in log-odds space. This has several advantages: it respects the multiplicative structure of probability (Bayes' rule updates are multiplicative), it prevents a single extreme forecast from dominating, and it produces better-calibrated aggregates when individual forecasts vary widely. Both the arithmetic and geometric mean produce valid probabilities, but the geometric mean is theoretically better motivated for probability aggregation.Question 24
In a $(3, 5)$ Shamir secret sharing scheme, how many shares are needed to reconstruct the secret?
A) 2 B) 3 C) 4 D) 5
Answer
**B) 3.** In a $(k, n)$ Shamir secret sharing scheme, $k$ is the threshold and $n$ is the total number of shares. The secret is encoded as a polynomial of degree $k-1$, and $k$ points uniquely determine a polynomial of degree $k-1$ via Lagrange interpolation. So in a $(3, 5)$ scheme, any 3 of the 5 shares are sufficient. Fewer than 3 shares reveal no information about the secret.Question 25
What distinguishes "computational zero-knowledge" from "statistical zero-knowledge"?
A) Computational ZK is faster to verify B) In computational ZK, the simulator's output is computationally indistinguishable from real proofs; in statistical ZK, it is statistically indistinguishable C) Computational ZK works on numbers while statistical ZK works on distributions D) There is no practical difference
Answer
**B) In computational ZK, the simulator's output is computationally indistinguishable from real proofs; in statistical ZK, it is statistically indistinguishable.** Computational zero-knowledge means that no polynomially bounded verifier can distinguish between real proofs and simulated ones. Statistical zero-knowledge provides a stronger guarantee: even an unbounded verifier cannot distinguish them (except with negligible probability). Statistical ZK is harder to achieve but provides stronger security. In practice, computational ZK is sufficient for most prediction market applications.Question 26
What role does "curriculum learning" play in training RL agents for prediction market trading?
A) It teaches the agent about market regulations B) It progressively increases the difficulty of the training environment C) It provides a structured set of historical trades for the agent to study D) It restricts the agent to trade only in educational markets first
Answer
**B) It progressively increases the difficulty of the training environment.** Curriculum learning starts the RL agent in simple environments (e.g., markets with predictable participants, short horizons, clear signals) and gradually increases complexity (more sophisticated opponents, longer horizons, noisier signals). This helps the agent learn basic trading strategies before confronting the full complexity of real markets, avoiding the sparse-reward problem where the agent never discovers profitable behavior.Question 27
A prediction market that uses "conditional markets" trades on:
A) Events that have already occurred B) The probability of an outcome given that a specific condition holds C) Events with uncertain resolution criteria D) Outcomes that depend on the number of participants
Answer
**B) The probability of an outcome given that a specific condition holds.** Conditional markets allow trading on questions like "What will GDP growth be IF Policy A is implemented?" The market prices represent conditional probabilities $P(Y | X)$. These are particularly valuable for policy analysis because comparing $P(Y | A)$ and $P(Y | B)$ provides an estimate of the causal effect of choosing A versus B, under certain assumptions.Question 28
What is the "sensitivity" $\Delta f$ in differential privacy?
A) How much the market price moves per trade B) The maximum change in the output of a function when a single individual's data changes C) The minimum detectable manipulation D) The probability of a privacy breach