Alternatives for prediction markets:

**Brier score loss:** $\frac{1}{N} \sum (y_i - \hat{p}_i)^2$. Sometimes used for calibration-focused training. - **Focal loss:** $-\alpha_t (1-\hat{p}_t)^\gamma \log(\hat{p}_t)$. Down-weights easy examples, focusing on hard-to-classify events. Useful for imbalanced prediction market outcomes.