March 24, 2019 Sunday
Bedtime Story
Termination of Rounds
Last night we saw that in the fourth round
of marriage proposal in our hypothetical village it was the rejected Richard
who was left to propose to leftover June.
For Richard June is the third choice when
it comes to women of the village and for June it is even worse; Richard is her
last choice of marriage amongst the men.
I hope you had given a little thought to it
last night.
Though not very thrilled June is left with
no option but to accept the only proposal that is coming to her even though it
is from Richard who is her last preference.
Remember, stable marriages do not mean
happy marriages and one must not confuse one with the other and this is a very
real-life scenario to that extent.
At this stage you as the yenta terminate
the process and seal the marriages and the fate of the four men and women.
The final configuration thus is:
Jenny(first)-Charles(first)
April(first)-Albert(second)
Lilly(first)-John(second) and
June(fourth)-Richard(third).
In the brackets those numbers denote the
rank of choice of the partner of opposite sex of their preference list that
each individual attained finally.
This is a stable configuration simply
because there are no unsatisfied men who have a better woman available to run
away with.
June has Richard with whom she cannot be
totally satisfied with but then there is no other man (namely Charles, Albert
and John) who has a partner that is ranked lower than June in his preference
list.
This means that neither Charles nor Albert
nor John would trade their partner for June.
Similarly there is no unsatisfied woman who
has an unfulfilled man who she can satisfy and therefore run away with.
Now I would like to point out at a point of
asymmetry between the two groups.
The most common question that is asked when
this solution is proposed is the optimality of the solution.
To grasp the significance of the question
of optimality one must understand first that there exists not one fixed set of
stable pairings for such a problem but many.
In other words the stable marriage problem
is not only solvable but can have multiple solutions that satisfy the condition
of stability.
So then this raises the question that whether
the solution or the matching done by the algorithm suits the men or women?
Or in other words is the algorithm fair to
everyone?
Please think about this question overnight.
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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