March 22, 2019 Friday
Bedtime Story
Demo of the Algorithm
At this stage you must terminate the
matchmaking process that you were asked to initiate.
The men and the women who are now paired
must be “locked” and they now have no further freedom to alter their choice.
The authors propose this to be a stable
solution.
The proof can be verified by trying out an
example by considering four fictitious men whose names are Richard, John,
Charles and Albert.
The women can be Jenny, Lilly, June and
April.
Now we can list out their preferences in
form of four by four columns.
In this table the men are listed on top
with four women listed below them in the order or decreasing preferences.
This means that given full freedom of
choice Richard would chose to marry Jenny the most and April the least (see the
column below).
You can also see that Jenny is the choice
number one for three men, namely Richard, Charles and Albert which is how it
often is in real life.
Richard John Charles Albert
Jenny April Jenny Jenny
Lilly Lilly April April
June Jenny Lilly Lilly
April June June June
In the same vein we will list out the
preferences of the four women for available men in the marriage market.
I have listed out the names of four women
on top below which are the names of whom are list of men in the order of
decreasing preferences.
This means Jenny would prefer to marry
Charles the most and Richard the least (see the table below).
This same preference hold true for June as
well.
Jenny June Lilly April
Charles
Charles John Albert
John John Charles Charles
Albert Albert Richard John
Richard Richard Albert Richard
This should be considered as the settings
for the algorithm to run upon.
With this we start the first round where
each man will propose to his first choice of woman.
This means that Richard proposes to Jenny,
John proposes to April, Charles proposes to Jenny and so does Albert.
You can see that Jenny receives three
proposals from Richard, Charles and Albert.
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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