A confidence interval on prediction-market concentration

What it measures

For each market we take every recorded trade, total each wallet's notional, and compute the Herfindahl-Hirschman Index of those volume shares: the sum of squared wallet shares of total notional. This is the standard concentration measure (the same index the US DOJ and FTC use in their Horizontal Merger Guidelines). A value near zero means volume is spread across many participants; a value near one means it is dominated by a few. We also report its reciprocal, the effective number of equally-sized participants, which is a transform of the index and not a head-count of real traders.

Concentration is a descriptive property of how trading volume is distributed. It is reported as a structural fact. It is not an assessment of whether any market or participant could move, or did move, prices.

How sure we are

The index is a number, but it is computed from a finite set of trades, so it carries sampling uncertainty. We report a 95 percent confidence interval on every estimate, computed by a Bayesian bootstrap that places Dirichlet weights on the fixed set of trades and recomputes the weighted index. We chose this scheme deliberately: the ordinary resample-with- replacement bootstrap is upward-biased for a concentration index, while the Dirichlet-weighted bootstrap preserves the trade support and gives a smooth, honest band. The point estimate and its interval and the method label always travel together.

The exact method is frozen and version-controlled. A change to the statistic, the resampling scheme, the bucket thresholds, or the cohort floor changes a published method hash, so any reported reading is reproducible and tamper-evident.

What the data shows

Across the 208 markets that clear the publishable cohort floor (at least 50,000 dollars of notional and at least 20 distinct wallets), the median concentration index is 0.26 and the 90th percentile is 0.87. Grouped by the single-largest wallet's share of volume:

• 12 diffuse (largest under 10 percent)
• 48 moderate (10 to 25 percent)
• 62 elevated (25 to 50 percent)
• 86 high (largest at or above 50 percent)

So in roughly 41 percent of these large markets a single wallet contributed at least half of the recorded trading volume. That is a fact about volume distribution. It is not a measure of manipulation or wash trading, and the most common benign explanation is a single liquidity-providing wallet, which the limitations below address.

What it does not do

• This read does not detect wash trading. The flow tape carries no counterparty linkage, so wash volume is not identifiable from it. Concentration is the v0 signal precisely because wash-share is not computable here.
• A high value is not evidence of wrongdoing and a low value is not a clean bill of health. A single market-maker or liquidity provider supplying most of a market's volume produces a high reading for an entirely benign reason. Both readings describe volume distribution only.
• No wallet is named or scored. The single-largest share is reported only as a coarse bucket, never as a raw number, so it cannot be re-joined to the public tape to point at one participant.
• The plug-in index is mildly upward-biased in very small or very diffuse markets (a property of the statistic, not the data). The point is reported for reproducibility and the interval for sampling uncertainty; the two can sit marginally apart in the most diffuse markets.