[EM] A question in classroom creation

[Michael A. Rouse]

Here's a rather different (and more complicated) voting problem than usual:

In the interest of classroom harmony, a school decides to let the 
children vote for which classmates they want in their home room. 
Assuming each class is the same size, what kind of ballot and what 
method of grouping students should be used? Also, should top-ranked 
(most liked) or bottom-ranked (most disliked) preference take precedence?

Some possibilities and problems that come to mind:
Ranked ballots  -- difficult to make it a "secret ballot," but it gives 
a fine-grained preference listing.
Approval/Anti-Approval -- rating classmates as approved, disapproved, 
and unknown. Also difficult to use with secret ballot. Probably the 
easiest to use.
Classroom grouping -- let students make their own classroom groupings 
(kind of like the districting problem), possibility of secret ballot but 
a *lot* of work.

If an example is needed -- and just to give some numbers -- let's say 
the school has 4 teachers and 100 students in the same grade, which 
would give 25 students per home room. For extra credit (heh), if they 
can also vote for which teacher they want, what would be the fairest way 
of resolving ties if more than one class prefers the same teacher?

This would also have an interesting application in voting district 
creation -- if voters can choose which precincts go into a voting 
district, what would be the fairest way of doing so?

Michael A. Rouse
mrouse1 at mrouse.com