Case Study 2: Addressing Inequality in Market Access

Overview

Prediction markets promise to aggregate the "wisdom of crowds" into accurate probability estimates. But whose wisdom is being aggregated? This case study examines the structural inequalities that shape participation in prediction markets, analyzes the consequences for market accuracy and social legitimacy, and evaluates concrete interventions designed to broaden access.

The Participation Gap

Empirical Evidence

Research on prediction market demographics consistently reveals stark participation imbalances. Data from Polymarket, PredictIt, Metaculus, and other platforms shows:

Gender. An estimated 85-90% of prediction market participants are male. This mirrors the broader pattern in financial trading and cryptocurrency adoption, but it is more extreme than many other financial markets (where women represent approximately 40% of retail stock investors).

Income and Wealth. Meaningful participation in real-money prediction markets requires disposable capital. Minimum deposits, gas fees (on blockchain platforms), and the opportunity cost of capital create a barrier that disproportionately excludes lower-income participants.

Geography. As documented in Chapter 38, regulatory restrictions and infrastructure barriers concentrate participation in North America, Europe, and parts of East Asia. South Asia, Africa, and Latin America are severely underrepresented despite comprising over half the world's population.

Education and Technical Literacy. Blockchain-based platforms require familiarity with cryptocurrency wallets, gas fees, and decentralized finance concepts. Even centralized platforms require financial literacy that is not universally distributed.

Age. Prediction markets skew young (25-45), excluding both older adults (who may have relevant life experience and domain expertise) and younger adults under 18 (who face legal restrictions).

Quantifying the Impact

Consider a prediction market on "Will there be a severe drought in Sub-Saharan Africa in 2026?" The people most likely to have relevant ground-truth information — farmers, local meteorologists, aid workers in the affected region — are precisely the people least likely to participate in the market. Meanwhile, traders in New York and London, who may have no direct knowledge of African agricultural conditions, dominate the price signal.

We can formalize this as an information loss problem. Let the total information about an event be $I_{\text{total}}$. The information accessible to prediction market participants is:

$$I_{\text{market}} = \sum_{i \in \text{participants}} I_i \cdot w_i$$

where $I_i$ is participant $i$'s private information and $w_i$ is their market weight (proportional to their position size). The information loss from participation inequality is:

$$\Delta I = I_{\text{total}} - I_{\text{market}}$$

If the excluded population holds information $I_{\text{excluded}}$ that is uncorrelated with the included population's information:

$$\Delta I \geq I_{\text{excluded}}$$

For questions about regions or communities that are underrepresented in the market, $I_{\text{excluded}}$ can be very large, making the market price a poor estimate of the true probability.

The Wealth-Weighted Voice Problem

Section 39.5.1 introduced the concept of wealth-weighted beliefs. We elaborate here with a concrete example.

Scenario: A prediction market on "Will a universal basic income pilot in City Y show positive employment effects?" attracts five participant groups:

Group Number Avg. Position Size Total Capital Belief (P(positive))
Hedge fund analysts 10 $50,000 | $500,000 0.30
Economics professors 20 $2,000 | $40,000 0.45
Policy researchers 30 $500 | $15,000 0.55
Local community members 100 $50 | $5,000 0.70
UBI pilot participants 50 $20 | $1,000 0.80

Wealth-weighted market price:

$$p^* = \frac{500{,}000 \times 0.30 + 40{,}000 \times 0.45 + 15{,}000 \times 0.55 + 5{,}000 \times 0.70 + 1{,}000 \times 0.80}{500{,}000 + 40{,}000 + 15{,}000 + 5{,}000 + 1{,}000}$$

$$p^* = \frac{150{,}000 + 18{,}000 + 8{,}250 + 3{,}500 + 800}{561{,}000} \approx 0.322$$

Equal-weighted average:

$$\bar{p} = \frac{10 \times 0.30 + 20 \times 0.45 + 30 \times 0.55 + 100 \times 0.70 + 50 \times 0.80}{210} \approx 0.637$$

The market price (0.322) is dramatically lower than the equal-weighted average (0.637). The hedge fund analysts, who represent less than 5% of participants, control 89% of the capital and thus dominate the price.

If the true probability is closer to 0.60 (as suggested by actual UBI pilot data), the wealth-weighted market is less accurate than a simple poll of the same participants. The market mechanism, which is supposed to improve on simple polling, actually performs worse because of the distortion introduced by wealth inequality.

Intervention Strategies

1. Subsidized Participation Credits

Concept: Provide prediction market "credits" (real or play money) to underrepresented populations, similar to food stamps or education vouchers.

Design considerations: - Targeting: Credits should be allocated based on demographic and geographic underrepresentation, not simply income. - Anti-gaming: Users must not be able to convert credits to cash immediately or create fake accounts to claim multiple allocations. - Market integrity: Credits must function identically to real money within the market (otherwise, credit-funded trades are discounted by other participants).

Pilot program design: - Budget: $500,000 per year - Target population: Residents of Sub-Saharan Africa with relevant expertise - Distribution: $100 per qualified participant (5,000 participants) - Markets: Focus on questions where local knowledge is valuable (food security, weather, public health) - Measurement: Compare market accuracy with and without subsidized participants

Expected outcomes: Based on analogies with subsidized participation in forecasting tournaments (e.g., Good Judgment Project's broad recruitment), accuracy improvements of 5-15% are plausible for questions where excluded populations have relevant information.

2. Play-Money and Reputation Markets

Concept: Remove the financial barrier entirely by using play money with reputation-based rewards.

Evidence: Platforms like Metaculus and Good Judgment Open demonstrate that play-money and reputation-based markets can produce accurate forecasts. The Hollywood Stock Exchange (play money) produced Oscar predictions that were competitive with real-money markets.

Advantages: - Zero financial barrier to entry - No regulatory barriers (play money markets are generally unregulated) - Broader demographic appeal - Reduced gambling harm risk

Disadvantages: - Weaker incentives for careful analysis - No financial "skin in the game" may reduce information revelation by those with costly private information - Harder to attract and retain participants long-term

Hybrid approach: Combine play-money markets with periodic prizes for top forecasters. This provides meaningful incentives without requiring financial investment from participants.

3. Quadratic Pricing Mechanisms

Concept: Make the cost of market influence grow quadratically with position size, so that small participants have disproportionate voice relative to their investment.

Under standard linear pricing, buying $n$ shares costs $n \times p$ (where $p$ is the price per share). Under quadratic pricing:

$$\text{Cost}(n) = n^2 \times c$$

where $c$ is a base cost parameter. This means buying 10 shares costs 100c, but buying 100 shares costs 10,000c (100x more, rather than 10x more under linear pricing).

Effect on the UBI example:

Under quadratic pricing, the hedge fund analyst who wants to invest $50,000 can only purchase $\sqrt{50{,}000/c}$ shares of influence, while the community member investing $50 purchases $\sqrt{50/c}$ shares. The ratio of influence is $\sqrt{50{,}000/50} \approx 32:1$, compared to $50{,}000/50 = 1{,}000:1$ under linear pricing.

Challenges: - Multiple account gaming: Wealthy participants can split positions across many accounts. - Market efficiency: Quadratic pricing prevents informed traders from fully expressing their views, potentially reducing accuracy for questions where financial sophistication correlates with information. - Implementation complexity: Requires robust identity verification to prevent sybil attacks.

4. Targeted Recruitment and Outreach

Concept: Actively recruit participants from underrepresented groups through partnerships with local organizations, universities, and professional networks.

Example programs: - Partner with agricultural cooperatives in Africa and South Asia to recruit farmers for food security prediction markets. - Partner with public health networks to recruit healthcare workers for pandemic prediction markets. - Partner with local government associations to recruit municipal officials for policy prediction markets.

Key success factors: - Language localization (not just English-language platforms) - Mobile-first design (many target populations have smartphones but not desktop computers) - Low bandwidth requirements (many target populations have limited internet access) - Cultural sensitivity (framing matters — "forecasting" may be more acceptable than "betting" in some cultures)

5. Structured Information Elicitation

Concept: Instead of relying solely on voluntary market trading, actively solicit forecasts from underrepresented groups through structured elicitation methods, then integrate these forecasts into the market price.

Methods: - Surveys with proper scoring rule incentives - Delphi-style iterative forecasting with feedback - Expert panels with diverse geographic and demographic representation - Peer prediction mechanisms (Chapter 41) for communities without easy access to trading platforms

Integration: The elicited forecasts can be incorporated into the market through subsidized market-making: a bot trades on the elicited forecasts, pushing the market price toward the inclusive consensus.

Case Example: The India Opinio Markets

India provides an interesting case study of inclusive prediction market design. Platforms like Probo and MPL Opinio have attracted millions of users by:

  1. Mobile-first design: These platforms are designed for smartphone use, recognizing that most Indian internet users access the web primarily through mobile devices.
  2. Vernacular language support: Offering markets in Hindi, Tamil, Telugu, and other regional languages.
  3. Small stakes: Allowing participation with as little as 1-5 rupees (approximately $0.01-0.06), removing the financial barrier.
  4. Culturally relevant topics: Offering markets on cricket, Bollywood, Indian elections, and other topics that resonate with local audiences.
  5. Legal framing: Positioning the platforms as "games of skill" under Indian law, avoiding the gambling classification.

Results: These platforms have achieved much broader demographic participation than Western prediction markets. However, they still face challenges with rural access, gender balance, and the quality of price signals in very low-liquidity markets.

Measuring Equity

The Representation Index

We define a Representation Index (RI) that measures how well a prediction market's participant base reflects the relevant population:

$$\text{RI} = 1 - \frac{1}{2} \sum_{g \in \text{groups}} |f_g^{\text{market}} - f_g^{\text{population}}|$$

where $f_g^{\text{market}}$ is the fraction of market participants from group $g$ and $f_g^{\text{population}}$ is the fraction of the relevant population from group $g$.

  • RI = 1.0: Perfect representation
  • RI = 0.5: Significant underrepresentation of some groups
  • RI = 0.0: Complete exclusion of half the population

The Accuracy-Equity Tradeoff

There is a genuine tension between accuracy and equity. In some cases, wealthy, well-informed traders produce more accurate forecasts than randomly selected members of the public. Diluting their influence with less-informed participants could reduce market accuracy.

However, this argument has limits:

  1. For questions where excluded populations have relevant information, broader participation improves accuracy.
  2. Even for questions where wealth correlates with information, the correlation is imperfect — excluding lower-income participants with genuine insights reduces accuracy.
  3. The legitimacy of prediction markets as a democratic information tool depends on broad representation.

The optimal approach is context-dependent: use quadratic or subsidized mechanisms for questions where broad representation matters (policy, social outcomes), and allow market-driven participation for questions where specialized financial knowledge is key (interest rates, commodity prices).

Discussion Questions

  1. Is it ethically acceptable for a prediction market to produce a wealth-weighted consensus on policy questions that affect everyone equally?

  2. How should prediction market platforms balance the accuracy benefits of allowing unlimited position sizes with the equity concerns of wealth-weighted voice?

  3. Would a prediction market that accurately reflects the beliefs of a narrow elite be more or less valuable than a less accurate market that reflects a broader population?

  4. How do we prevent subsidized participation programs from being gamed by sophisticated actors who create fake identities to claim multiple subsidies?

  5. Does the existence of play-money alternatives (Metaculus, Good Judgment Open) adequately address the equity concerns about real-money markets, or are the two types of markets fundamentally different in their social function?

Computational Exercise

See code/case-study-code.py for a simulation that: 1. Generates a population with heterogeneous wealth, information, and beliefs. 2. Simulates a prediction market under linear pricing, quadratic pricing, and subsidized participation. 3. Measures accuracy and representation under each mechanism. 4. Identifies the conditions under which broader participation improves accuracy versus reducing it.