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I have two algorithms that produce, for every observation, a vector of probabilities for 3 classes

           | Algo 1           | Algo 2
-------------------------------------------------
Obs 1      | [0.5, 0.3, 0.2]  | [0.3, 0.3, 0.4]
Obs 2      | [0.3, 0.2, 0.5]  | [0.1, 0.1, 0.8]
Obs 3      | [0.2, 0.2, 0.6]  | [0.2, 0.4, 0.4]
....

I want to compare how similar the algorithms are. One simple approach is to convert the probability vectors into the winning class and evaluate a simple Accuracy, i.e. # of match / # observations.

Is there a measure or statistical test that can compare the probability vectors?

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