How fast does a prediction market converge when traders only understand part of it?

research/market-subspace-descent

Convergence of cost-function markets with partially informed traders as randomized subspace descent: maker loss telescopes to ½(e₀'Ae₀−e_T'Ae_T), closed-form slowdown from correlated securities (31→356 rounds at c=0.95, d=5), A-conjugate bundles restore 1−1/d exactly, noisy-belief step size is an SGD step (running mean beats best constant step), LMSR simulation checks the local rates.

11 tests

What it found

Traders who each move prices within a subspace of securities make a cost-function market a randomized subspace descent. The market maker’s expected loss telescopes to ½(e₀′Ae₀ − e_T′Ae_T) whoever trades, so accuracy is bought once. Correlated securities slow single-security traders in closed form (5 securities: 31 rounds to reach 10⁻³ of the error uncorrelated, 356 at correlation 0.95), while offering A-conjugate bundles restores the exact rate 1−1/d at any correlation. With noisy beliefs the fraction κ a trader moves acts as an SGD step size: floor dκσ²/(2−κ), and a per-security running-mean step beats the best constant step (error 0.26 vs 0.47 at 100 rounds; full steps stay at 5). A simulated 4-outcome LMSR matches the local rate predictions to within 0.01 for two of three bundle designs and is faster than predicted for the third, for a reason not isolated. Quadratic-cost theory with i.i.d. trader arrival and Gaussian belief noise.

A figure from its own output

Figure produced by research/market-subspace-descent: correlation_rate — market-subspace-descent/experiments/correlation_rate.svg, written by the project's own experiment code.

Paper, code and results

More in Prediction-market design

What does a constant-product pool concede to informed traders?Constant-product AMMs as cost-function prediction markets: worst-case loss C0 never attained, informed-trader profit exactly C0(1−n·GM(π)) (ratio to LMSR → ln n, crossover at n=e), polynomial price tails (p=0.999 costs 3.4× LMSR), exact regret identity, no forgiveness gain under regime switches.
What does not knowing the horizon cost a market maker?LMSR with time-varying liquidity as anytime Hedge: b_t = c*√t costs exactly √2 over the horizon-aware bound, doubling is 1.70× worse, and self-tuning liquidity makes the subsidy equal the accumulated mixability gap (1.3 vs 102 on easy data).
The subsidy cost of privacy in prediction marketsDifferentially private LMSR via the binary-tree mechanism: path-wise loss bound, and the accuracy/subsidy cost of privacy.
Who pays for the information in a manipulated market?Manipulating an LMSR verification market: manipulator loss b·KL(q‖τ) equals the extra informed rent, and manipulation raises accuracy only in a liquidity band (thin: costs 1−2q; deep: neutral).
What does a slippage limit give away in a prediction market?Sandwiching an LMSR verification market: attacker profit is exactly the victim's slippage tolerance times its fair cost, needs capital ≈ εb/(1−p), dies to a fee ≈ v(1−p)/(2b); pro-rata batching keeps 99% of the extraction, random ordering cuts it 3×.
Who trades decides how liquid a verification market should beGlosten–Milgrom vs LMSR for a verification market: informed share fixes b* = 1/(2 atanh m) (verified to 2e-16), peak misspecification regret is scale-free and overconfident b costs 1.5–2.4× more, LMSR subsidy → b* ln 2 is the spread GM charges.

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Proper scoring & elicitation28 Effort & peer prediction9 Verification games & slashing19 Detection & tolerances14 Markets as routers13 Prediction-market design9 Paying contributors8 Decentralised training systems23 Digital twins & sim-to-real164 LLM chip design loops40 Robot manufacturing loops53 Ambient AI assistant46 Self-replicating manufacturing34 Simulation-first design64 Engineered clothing45 Task-specific AI accelerators40 Algorithmic chip-design loops42 Open-source purpose-built robots44 The software-engineering loop43 Adversarial human imitation41 Open-source residential construction41 Autonomous multi-angle capture34 Sensing, imaging and 3D31 Energy supply and dense energy storage39 Robot societies among people31 Agentic co-design of low-cost robots27 Laundry-hanging robots25 Machine learning on qualitative data23 Robots on the building site27 Civilizations & group psychology1 History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.