The subsidy cost of privacy in prediction markets

research/private-markets

Differentially private LMSR via the binary-tree mechanism: path-wise loss bound, and the accuracy/subsidy cost of privacy.

6 tests

What it found

Differentially private LMSR via the binary-tree mechanism: error scales as 1/(bε), tree noise beats per-release noise ~15×, and privacy noise is exploitable so market-maker loss far exceeds b ln 2. Stylised.

A figure from its own output

Figure produced by research/private-markets: accuracy — private-markets/experiments/accuracy.svg, written by the project's own experiment code.

Paper, code and results

More in Prediction-market design

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.
What does a fee do to a prediction market’s price?Proportional fees on an LMSR verification market: exact no-trade band [q/(1+f),(q+f)/(1+f)], price lag q/(1+f), dead-market cliff f ≥ 2a−1 (threshold 2 atanh f at ½), exact fee revenue f·b·ln((1−p₀)/(1−p_T)), and a break-even fee that costs +38% Brier error.
What is a seat in a prediction market worth?Sequential LMSR seat rents are conditional mutual information: they telescope to the maker's expected loss (≤ b ln 2), fall with position at the Chernoff rate, order only redistributes a fixed total, and entry costs make error fall only ~1/b in the subsidy.
How fast does a prediction market converge when traders only understand part of it?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.

All 9 Prediction-market design projects →

Other research topics

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.