How to combine soft-max value from two or more neural networks

Consider a scenario where we have some input variable $X$ (maybe an image), which goes through several noisy path and we generate $K$ noisy observations: \begin{align} Y_i = X_i +Z_i, i \in \{1,\ldots, K\} \end{align} where noises are independent. Here I am assuming additive structure but it doesn't have to be. Suppose that I use the same neural network on $Y_i$ 's to classify. Also, suppose that I have access to the soft-max values In particular, let $p_i$ be the soft-max value for input $Y_i$ , Question: How do I combine these values in the best way to determine my class? One option is \begin{align} p_{new} = \frac{1}{K} \sum_{i=1}^K p_i \end{align} One can also just threshold at $0.5$ and find the majority. I am looking for an answer that would have some theoretical backing.