Interesting task!
Unless there's some whitepaper out there explaining the "real" right answer,
Cameron's mention of how to test the effectiveness is great.
One way that occurred to me is have a meta table with a column for
attribute-name and a column with the value of importance (would be
sequential, with 1 being least important) - Ill call it tA for this email...
Step 1
ColumnList = [all columns from Ta]
Select #ColumnList#, count() from student group by #ColumnList#
Take the returning row with the smallest count
memberPool = any member that match all the columns in #ColumnList# into each
group
insert (memberPool/number of groups) members into each group-member
Step 2 - loop over this
ColumnList = [all columns from Ta] with importance > loopcount
Select #ColumnList#, count() from student join group-member group by
#ColumnList# -
Take the returning row with the smallest count
memberPool = any member that match all the columns in #ColumnList# and not
in group-member into each group
break loop when all members are assigned
The importance might already be determined arbitrarily (which by that I mean
for some non-data/math reason).
If it weren't, maybe do this:
For each column in ColumnList = [all columns from Ta]
Select '#column#',#column#,count from member group by #column#
after looping, the column with the highest count
UNION ALL (repeat loop)
Out Of this set, whichever column/value pair has the largest count, use that
for your most important, for your second most important, use the pair with
the next-largest count and not matching the column you just said was most
important... and so forth.
Not sure how any of that would pan out... but my two cents!
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Cameron
Childress
Sent: Friday, July 25, 2008 18:44
To: discussion@acfug.org
Subject: Re: [ACFUG Discuss] sorting question
Dean's method is one possibility. This is actually a very interesting
question and I'm nojt sure how I'd solve it. I thought about it a bit
during my drive home, and here's the approach I would take... This is
alot easier if there are only two choices for each statistic
(male|female - american|foreign - white|nonwhite), but it could also
work with multiple choices for each.
First, how to measure the success of the program? Measure the
percentage of each stat in the group as a whole (I'll call this Big
Ratio), and then measure the percentages in each of the 25 groups
(I'll call this Group Ratio) and see how closely they each match.
Okay, next, how to divide them up into groups? I'd start by seeding
each group with a random individual. Then I would take each person
from the pool of potential students and loop over each group, testing
to see if adding that person to that group would make the Group Ratio
for that group closer or farther away from the Big Ratio. Whichever
Group Ratio moves the farthest toward the Big Ratio would be the group
you add that individual to. Once a group reaches 17 people, close it
and stop adding people to it.
You'll have to find a way of combining the ratios and determining one
big number that represents the combination. I am sure if I paid more
attention in my statistics class I'd know it had something to do with
standard deviations, but I didn't pay any attention - so that's up to
you to figure out.
Once you are done, look at all the Group Ratios and see how close
their balance measures up to the Big Ratio.
Two suggestions to make this easier on yourself:
1) Start by attempting to balance a smaller number of groups than 25.
2 or 3 maybe.
2) Start with binary choices, then move on to multiple choices after
you have amethod that is capible of balancing two choices.
Least that's where I would start. If you are willing, post your
solution (in english or in code) once you're done. I would be
interested in seeing how you did it.
-Cameron
On Fri, Jul 25, 2008 at 5:25 PM, Tepfer, Seth <[EMAIL PROTECTED]> wrote:
> I have a challenge laid out before me. I need to divide the incoming
Oxford student class into 25 groups of about 16 or 17 students each.
However, they want the groups to be as balanced as possible, across number,
sex, race, and geographic origin. Now, I can easily see how to balance based
on sex or any single characteristic. But how to balance across all three at
the same time? My head starts spinning when I think about the issues that we
won't necessarily have equal distribution across any of the characteristics.
>
> I don't need the code, just the concept. I am having a hard time
conceiving on how to do this if the people were standing in front of me,
much less by code. Any ideas?
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