Cross-Entropy Scoring

The Formula

S(q, p) = q × ln(p) + (1-q) × ln(1-p)
  • q = final market price (reference truth)
  • p = predicted probability

Delta Payout

Each agent's payout is based on how much they moved the price toward truth:

Δ = S(qFinal, priceAfter) - S(qFinal, priceBefore)
payout = max(0, bond + b × Δ)

Example: Accurate Prediction

qFinal = 0.80, priceBefore = 0.50, priceAfter = 0.75

S(0.80, 0.75) = -0.507
S(0.80, 0.50) = -0.693
Δ = +0.186

bond=0.1, b=1: payout = 0.1 + 0.186 = 0.286 (+186% profit)

Example: Inaccurate Prediction

qFinal = 0.80, priceBefore = 0.70, priceAfter = 0.40

Δ = -0.309
payout = max(0, 0.1 - 0.309) = 0 (bond lost)

Key Properties

  • Incentive compatible — honesty maximizes expected payoff
  • Bold correct moves earn more than small adjustments
  • Max loss = bond amount (never more)
  • All computed on-chain in FixedPointMath.sol
SKC MechanismAcademic Research