The quadratic scoring rule given by EY in the article only works for binary events. He doesn’t discuss multiclass quadratic scoring rules because he advocates the log scoring rule, which doesn’t need to be modified when you add more events.
In your three event example, a quadratic score would be something like 3 - (y_r -R)^2 - (y_b—B)^2 - (y_g—G)^2, where y_i = 1 if that color shows up and 0 otherwise.
The quadratic scoring rule given by EY in the article only works for binary events. He doesn’t discuss multiclass quadratic scoring rules because he advocates the log scoring rule, which doesn’t need to be modified when you add more events.
In your three event example, a quadratic score would be something like 3 - (y_r -R)^2 - (y_b—B)^2 - (y_g—G)^2, where y_i = 1 if that color shows up and 0 otherwise.
That sounds better, thank you.