I have a problem on my hands, and would like help matching it to the existing, studied problems. I explain it like so:
I have a sequence of $n$ equal-sized glasses of water. Each has a different amount of water inside, some are very full, some are near empty, and some completely empty. I can pour water from one glass into another, but have no way of measuring how much water each pour removes/adds from the glasses. I can only perform a pour and then compare the levels of the glasses again. Pours are "atomic", meaning a roughly fixed amount of water is transferred with each one (I cannot make pours of different sizes). What steps do I need to follow to equally distribute all the water among the glasses?
An initial algorithm I have come up with is to sort the glasses in order of fullness. Then I take the most and least full, and do one pour of water. I repeat, again taking the least full glass and the most full glass, and doing one pour. Repeat until all glasses are roughly equal.
Does a general problem exist that is similar to this?
In the interest of avoiding the XY problem, here is the reason I am interested in this: I am writing a routine that iteratively adjusts the probability thresholds for multinomial classification. I can nudge each threshold in either direction, and my aim is to have each class be equally likely. However, I will not know what impact each "nudge" has until I've done it, re-fitted the classifier and gotten predictions. I then use the outputted predictions to calculate the probability of each class. The above explanation is my attempt to describe what I need it to do.