What does it cost to route between models with conditional markets, and what does a stake do to the answer?

research/decision-markets

Conditional markets that route between models: inverse-propensity Brier is proper even when the router reads the report, exploration costs exactly 1+(K−1)e^{ω²/2τ²} in payment variance (probit: infinite for τ ≤ ω), and a stake gap distorts the reported gap by a closed-form fixed point with second-order harm.

16 tests

What it found

Markets that forecast each model’s loss if chosen only ever see the chosen arm. An inverse-propensity Brier payment is exactly proper even when the router reads the report (without the weight a trader shades its forecast, or hides), and its price is exact: E[1/π] = 1+(K−1)e^ω²/2τ², so payment variance blows up as the router cools (a probit router has infinite variance for τ ≤ ω; Monte Carlo at τ=0.3 sees 29 against the exact 195). Exploration regret is at most 0.2785τ. Equal owner stakes cancel in the decision, a stake gap shifts the reported gap by a closed-form fixed point, and the loss it causes is second order, ∝(ΔB/k)². Gaussian, one-shot, stylised.

A figure from its own output

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

Paper, code and results

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All 13 Markets as routers projects →

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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.