March 27, 2019 Wednesday
Bedtime Story
"Some Practical Questions" - 2
Tonight we shall continue with the part of
the paper that was written under the heading of ‘Some Practical Questions’.
It is extremely interesting to note the
inputs the authors are suggesting to make the algorithm workable in real life
scenario which is rather uncharacteristic of pure mathematicians who generally
do not care if their mathematics finds any use or applications.
This aberrant behavior from these
mathematicians could be due to the fact that they were also economists who in
contrast to their mathematical counterparts do really care for the implications
of their theory to the real world.
“An obvious modification would be to
collect all relevant information at some central clearing house, and have an electronic
computer run through the motions of “application”, “rejection”, “placement on a
waiting list”, etc.
The only drawback to this solution is the
enormous amount of effort that would be expended by the participants in making
up their complete preference orderings, most of it completely wasted.
There would be no time for careful
consideration of alternatives, by either the colleges or the applicants.
This indicates that some sort of compromise
between complete mechanization and no mechanization would have the best chance
of success, with the candidates submitting to the clearing house only their top
four or five choices (say) at the start.
In this connection the following
observation is of interest: It is not essential in our procedure for a rejected
applicant to apply immediately to the next college of his choice.
The final outcome is not changed if he
“sits out” one or more rounds while other rejectees are making new
applications.
This means that the whole process would not
have to grind to a halt whenever a single individual’s partial list of
preferences happens to be exhausted through repeated rejections.
There are several other complicating
factors aside from the sheer magnitude of the computation.
One of them is that admission, or the
acceptance of admission, is often tied in with other things, like the award of
financial aid, advanced academic standing, or the like.
The college’s scholarship budget
constitutes a new constraint, comparable to the quota q, and a more elaborate
mathematical model would clearly be called for.
An adequate theory would have to cope up
with such details as scholarship awards of different sizes, or students who
would rather to a college A without a scholarship than to college B with one.
Also, some colleges might prefer to give a
poor boy a scholarship rather than admit a better-qualified rich boy and have
money left over.
Still another problem is presented by
colleges that pay attention to overall composition of the entire class.
Their preference scales are obviously more
complex than a simple ranking of individual applicants.”
Stay tuned to the voice of an
average story storytelling chimpanzee or login at http://panarrans.blogspot.com
Good night Mon Ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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