March 28, 2019 Thursday
Bedtime Story
"Some Practical Questions" - 3
Tonight we shall continue with the part of
the paper that was written under the heading of ‘Some Practical Questions’
“To meet this situation a further
generalization of our theory is called for, particularly in the definition of
stability.
While it is not clear that either of the
generalizations indicated above can be formulated in such a way as to preserve
the content of Theorems 1 and 2, it is the authors’ opinion that the “deferred
acceptance” idea, insofar as it can be made practicable, is capable of
producing assignments that are markedly superior to those obtained under the
present system, or lack of system.
The two important points at which “deferred
acceptance” differed from current practice are the following:
(1) Applicants are assured that they run no
risk of losing out on their lower choices by default while their higher choices
are being considered, and
(2) Colleges are assured that the
candidates on their waiting lists have no other applications pending: if
offered admission they will accept it.”
From this paragraph of the paper you can
get a fair idea about the grave doubts that the authors themselves were casting
as to the practicality of their theoretical solution or the algorithm to the application
in the real world matching program of the resident doctors of the United States.
Yet the algorithm was in place 10 years (1952)
before the paper saw the light of day.
So probably what the paper did was to
confirm and validate the accuracy and fairness of the algorithm in assigning
the right colleges to the residents.
Later a correspondence published in 1981
titled “An analysis of the Resident Match” in the New England Journal of
Medicine affirmed the algorithm in use was an optimal program for the
applicants.
Later in 1995 the Board of Directors of the
National Residency Matching Program commissioned a research study into the
matching program and the algorithm used for it.
They desired to know if any new and better
form of algorithm existed that should replace the existing one.
Eventually in the May of 1997 the existing
algorithm was replaced with a new applicant-proposing algorithm and is in place
since then.
Comparisons done later and retrospectively
in the matching outcomes between the older and the newer algorithm suggested
there was not much of a difference in the net outcome by the new algorithm.
We have gone through the essence of the
entire paper and are left with a fairly decent understanding of the problem,
its solution and its application to one real-case scenario.
Now is the time (last but not the least as
the idiom or the expression goes) to state the actual formal algorithm whose
function would be to attain a stable set of marriage pairs.
We can label this function as
StableMatching.
I am ignorant of all programming languages
and the only one I ever learnt is the BASIC language back in 1985.
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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