A market on how wrong the market is.

Simple assumes nothing

A prediction market gives you a probability. The natural next question is how much to trust it, and the prediction market answer to any question is to open a market on it. So you open a second market on whether the first one is close to right.

Then the same question applies to the second market, so you open a third. You can keep going as long as you like. The structure loops back on itself, which is where it stops being a gimmick.

Three things could happen. Each layer corrects the one beneath it and the whole tower settles on the truth, which would be a self-healing oracle and genuinely useful. Or the layers push each other back and forth and never settle. Or noise compounds upward until the whole thing means nothing. Nobody has built one to find out.

Moderate assumes you know what a market is

Concretely: layer 0 is a real event. Layer 1 is an LMSR market on that event. Layer 2 is an LMSR market on whether layer 1's terminal price lands within 5% of the true probability. Layer 3 prices layer 2's accuracy. Each layer's resolution depends on the layer below, so information flows up and incentives flow down.

Reframed, layer 2 is trading the volatility of a probability rather than an outcome. A VIX for prediction markets. That framing turns it into a product rather than only a theory question, which matters for whether anyone ever trades it.

Four parameters should decide the behaviour: how many agents, how good their information is, how much liquidity sits at each layer, and how correlated the traders are. Correlation is the one I would watch, because correlated traders are the most plausible route from convergence into oscillation. Hanson flagged indefinitely recursive jury mechanisms as an open question and left it there. This is my picked direction and I have published nothing on it, which is the largest gap between what I have thought about and what I have said out loud.

Technical state of the art and the gap

The formal question is whether the layer map is a contraction. If the map from layer n's price vector to layer n+1's is a contraction on a complete metric space, Banach gives a unique fixed point and convergence from any starting configuration, which is the self-healing oracle result. The conditions under which it contracts are unknown. LMSR's cost function curvature is the obvious place to look, since b controls how far a given order moves the price and therefore how strongly one layer transmits to the next.

The result worth having is a phase diagram. Axes: agent count, information quality, liquidity ratio between layers, trader correlation. Regions: convergence, limit cycle, divergence. Finding and characterising that boundary is the paper, in the same sense that a pressure-temperature diagram is the answer for phase transitions in water.

Spec problems sit underneath all of it and need settling first. What exactly does a layer 2 contract pay out on, over what horizon, and does the lag between layers create an exploitable incentive? Is the relationship between layers self-reference or principal-agent? Those choices change the mechanism, so simulation results mean little until they are pinned down.

Smallest useful version: a three-layer toy in code with synthetic agents, sweeping two parameters. A weekend for the first plot, a month for a defensible one.