[EM] update on classroom creation question

[James Green-Armytage]

On April 16, Michael Rouse asked a question about classroom creation. 

I replied (in part) as follows:
>Proposal 1: Use a range ballot, e.g. integers from -3 to 3 inclusive. 
>	Consider every possible arrangement of children into the 4 classes. 
>	Give each possible arrangement a score as follows: Measure each child's
>utility as the sum of his rating of all other children in the class. Sum
>the utility scores for each child to find the total utility of the
>arrangement.
>	Choose the arrangement with the highest total utility. (If multiple
>arrangements are tied, choose randomly between the arrangements with the
>highest score.)
...
>
>Commentary:
>	This method, while perhaps optimal from a results point of view, seems
>like it would take a lot of computing power. 

	At this point I'd just like to add that, if considering all possible
outcomes is too computationally expensive (which seems likely when one is
working on the scale of Ted's 100-student/4-class example), one should be
able to get results of comparable quality by considering a large number of
randomly generated outcomes.
	Additionally, one could employ various non-random and/or semi-random
methods of constructing outcomes, while still using the proposal above to
evaluate them. 

my best,
James