Combine two different multi classification models for better prediction

Question

I have two different multi-classification models on the same dataset. Since both use the same dataset, input and output are the same.

For example, given input x, model A and B output like the below.

M1(x) => S2(0.3), S4(0.6), S7(0.1)
M2(x) => S1(0.1), S2(0.7), S7(0.2)

Given this result, I would like to re-order the result, e.g., S2(0.5), S7(0.3), S2(0.1), S4(0.1).

I am not sure that what kind of machine learning techniques are used in this re-ordering. I can imagine that linear regression can be used as follows:

S1_final = w1 * S1_fromM1 + w2 * S1_fromM2 + w2 * some_features

Do you know that is there any techniques combining two probabilities? This may be called ensemble learning, though, my two models are differently trained on the same dataset.h

Answer 1

Average probability is one and one could be to use multinomial regression with probabilities as components of input vector and have also true class labels which are predicted.

And neural network could be used with similar effect.