In many practical situations, we only know the interval containing the quantity of interest, we have no information about the probability of different values within this interval. In contrast to the cases when we know the distributions and can thus use Monte-Carlo simulations, processing such interval uncertainty is difficult -- crudely speaking, because we need to try all possible distributions on this interval. Sometimes, the problem can be simplified: namely, it is possible to select a single distribution (or a small family of distributions) whose analysis provides a good understanding of the situation. The most known case is when we use the Maximum Entropy approach and get the uniform distribution on the interval. Interesting, sensitivity analysis -- which has completely different objectives -- leads to selection of the same uniform distribution. In this paper, we provide a general explanation of why uniform distribution appears in different situations -- namely, it appears every time we have a permutation-invariant objective functions with the unique optimum. We also discuss what happens if there are several optima.