Signal Normalization & Scoring
Raw variance signals and regime-based divergences are not directly comparable across markets. Prediction markets differ in liquidity, time-to-expiry, activity level, and volatility. Feature 3 defines how Variance Markets converts heterogeneous regime divergence signals into standardized variance scores that can be compared, ranked, and consumed consistently across the protocol.
The goal of this feature is not to amplify signals, but to make them scale-invariant, market-agnostic, and stable.
Why Normalization Is Required
Without normalization:
highly liquid markets dominate signals
volatile markets appear artificially “high variance”
long-duration markets accumulate more divergence by default
short-lived markets are underrepresented
Variance Markets explicitly avoids this bias. A variance signal should represent structural disagreement, not market size or noise.
Inputs to the Normalization Layer
For each market derived from Polymarket, Feature 3 consumes:
regime-conditioned probability estimates p_ri(t)
regime-to-regime divergence values V_ij(t)
cumulative divergence over time
market liquidity metrics
remaining time until resolution
sampling density and activity level
All inputs are produced by Feature 1 and Feature 2 and are deterministic given public data.
Time Normalization
Variance accumulation is normalized by market lifetime to prevent long-running markets from dominating scores.
For a market active between t0 and t1:
raw cumulative divergence is divided by (t1 − t0)
resulting values represent divergence intensity per unit time
This ensures that variance scores reflect how strongly beliefs diverge, not how long a market has existed.
Liquidity Normalization
Markets with deeper liquidity naturally absorb disagreement with smaller price movements. To avoid penalizing liquid markets or overvaluing thin ones, divergence signals are scaled by a liquidity adjustment factor.
Conceptually:
high-liquidity markets require stronger conviction to move
low-liquidity markets move easily and are down-weighted
This produces variance scores that are conviction-adjusted, not price-sensitive.
Regime Weighting
Not all regimes contribute equally to meaningful variance.
Regime contributions are weighted by:
regime confidence scores
persistence duration
stability over time
Transient or low-confidence regimes contribute less to the final score. Stable, persistent regimes contribute more. This prevents short-lived noise from dominating variance metrics.
Variance Score Construction
After normalization, a single variance score is produced per market and per observation window.
The score represents:
the magnitude of disagreement between regimes
adjusted for time, liquidity, and regime confidence
Scores are bounded to a fixed range to ensure:
comparability across markets
compatibility with downstream products
stable interpretation over time
A higher score indicates stronger and more persistent belief divergence. A lower score indicates consensus or rapid convergence.
Output of This Feature
Feature 3 outputs:
normalized variance scores per market
regime-weighted divergence metrics
time-adjusted variance intensity values
comparable rankings across markets
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