A confidence interval on prediction-market concentration

What it measures

For each market we take every trade in Convexly's recorded participant flow, total each wallet's notional, and compute the Herfindahl-Hirschman Index of those volume shares: the sum of squared wallet shares of recorded notional. That record is a periodic sample of venue trades rather than a complete trade record, so the index describes the sample. 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 recorded notional and at least 20 distinct recorded wallets), the median concentration index of the recorded flow is 0.26 and the 90th percentile is 0.87. Both the floor and the index are computed on a periodic sample of venue trades, not on a complete trade record, so each figure describes that sample and not the market. Grouped by the single-largest wallet's share of recorded 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 markets a single wallet contributed at least half of the trading volume Convexly recorded. Whether that wallet contributed at least half of the market's actual volume is a different question, and the recorded sample cannot answer it. That is a fact about the distribution of recorded volume. 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

• These figures are computed on Convexly's recorded participant flow, which is a periodic sample of venue trades and not a complete trade record. The record is assembled by polling a bounded number of the most recent trades on a fixed schedule, so it favors recent activity and wallets that trade frequently. Concentration computed on a sample of a market's trades is not that market's concentration, and because the sample is not uniform the gap between the two is not mean-zero sampling error: the reading may be biased in either direction, by an amount this page does not measure. Read every number here as a property of the recorded sample.
• This read does not detect wash trading. The recorded flow 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.