I recently asked this question:
I realized that my question was not asked very clearly. So here is another way to phrase the question:
I have ten objects. With a different independent scale for each object, I measure their weights 100 times each (1000 measurements in total). I can compute the variance $\sigma^2_i$ of each of the scales based on the distribution of the measurements of each object.
Given my measurements and my $\sigma^2_i$, what is the probability for each of the objects being, in fact, the heaviest?
Thank you for your help!