Is there a thing called a stable marriage and relation ?? - Part 1

Disclaimer: This is more of a mathematical and logical analysis of marriage. This is for rational audience who can enjoy a piece of logic with out any involvement of emotion. Or rather some logical analysis of how relations, trust etc involuntarily get biased by numbers and probability. Normal (non engneer, non scientific-mathematical audience might find it a boring read. But even others might find it as boring! :D )
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Assumptions:

1.  All men and woman are straight
2. all men and woman appear in the "desired" list of each other with some weight. e.g. Some men may be 99% desirable for woman X and some may be just 0.001% for X and vice versa. But every one appears on the desirable list of each other.
3. We have not taken into account the possibility of preference change after they are coupled. (this will over complicate the situation :P) (this will be covered in part 2 of this research.)

Definition:

An unstable marriage: When given a married pair, X-a and Y-b, if man X prefers another woman 'b' more than his current wife 'a' and woman b prefers X more than her current man Y, then X-b is called a unstable pair. 

Any pair (X-Y) when not an element of the "unstable" set is said to be a stable pair.
Lets see:
Assume we have a sample set of 26 males marked as A,B,C,D....Z and a sample of 26 females marked as a,b,c,d....z.
Ask each of the man and woman to form a list desired partner in the order of precedence.
For example the list may look something like this:
Male                                             Female
-----                                             --------
A: b,s,d,c....                                 a: C,D,B,Z....
B: b,a,c,t....                                  b: A,P,C,W...
C:a,b,c,r....                                  c: B,D,S,T....   
(This just an example combination shown here)

Now our job is to find how many "stable pair" can be formed which can result in a happy and trustworthy marriage. One of such approach as it would occur to mind first is to  go on forming pairs based on the preference list. Call a pair when a mutual inclusion of male,female exist in their preference list high on precedence. And swap it when encounter a yet higher mutual precedence. Example: Initially (B-c) will be paired but later their partners can be swapped and they may form a more stable pair like (C-a) and (B-c)
This seems working here but it may lead to re-swap and hence form an infinite loop on a bigger data set.
So lets first solve the problem at hand to form stable couples set:
pick an unpaired male X and the list female x on his list(first preference)
remove x from his list and check if x is already paired
if already paired then check if X appeared on a higher precedence then x's current partner in her list (if x is unpaired then pair up X-x for now)
          if yes then pair up x with X and continue with the next male.
else if X does not appear on a higher precedence on x's list as compared to her current partner then pick next female on X's preference list.
Now so far so good! We feel we can actually form a stable marriage and stay happy(works for an arranged marriage). But in a real world we don't run such an exercise while considering to get married. So I tried to just have some data around it and apply for game theory to see what might be the trend look like if we consider married people or people newly in love and assign a weight to their trust and relation how would it look like. I asked a few people to answer a few questions:
1. What their dream partner attributes look like
2. How often they end up admiring some one from opposite gender cause he/she matched with some of the attributes they admire are present in them?
3. How many such people are around them in acquaintance circle who can match their criteria?
4. What is the attribute precedence list look like for them?
and few other question which were little private and optional for them to answer like their sexual behavior and compromising point of "more-moral-ego-based-attribute" to a "more-materialistic-based-attribute" Like a happy charming fellow's charm compromised to someone else's salary etc.

One I had the answers to these questions. My job was to do a little research to find out from their Facebook behavior what they tend to like + how many guys at least I think match their criteria. And once let us say paired, what are the emotional, geographical exposure they will have to the other potential matches we had found earlier. All these taken into consideration with the futuristic projection of the change in the "desired attributes" in the partner and other potential candidates makes a recipe for stable and trustworthy relation! Lets take an example first of Male A and female 'c':

Male A say is paired with female 'c'. Male A's criteria looked like
- Good looks, decently educated, fair skinned, lovable, belonging to a reputed family background, easy going, working
- With these criteria he got married to female 'c'.  Attributes female c had in reality - good looks, fair skin, a well earning day job, higher educated, independent mind and lifestyle, easy going.
- 'c' had criteria of a match as - presentable, tall, secure job, good sense of humor, dependable background with handsome earnings, extrovert.
Attributes male A had in reality - Good looks, tall, handsome earning, not that dependable background, extrovert with a big friend circle, high educated, secure but frequently travelling job.
Female 'c' has exposure to matching criteria males in job, from past friends, in society she lives.
Male A has exposure to matching criteria females in cities he travels to, from past friends, in society he lives, in parties etc (as he is extrovert and has a huge friend group).

Let us say these criteria changed in both partner's after few years the female stopped working or male lost job, male/female or both deteriorated in looks, easy going became tough given social complexities.

In such a situation the probability of choosing another partner becomes prominent. Lets see how prominent by applying some game theory to it. And lets see should one break the trust in a situation like above?

N.B. (I will post a follow up on this today. Either will update the same blog or post a new one on top of this. As its growing big, am breaking it into two. :) till then keep wondering and let me know your guess to the above question in the comments.

Truly
Abinash

Why me?

"Why this has to happen at all.." he sniffed. "I have been a loving father, a caring husband and a hardworking man. Then why me? So many people in the world overlook their fundamental family and social responsibilities. So many people breach rules, behave violently posing a threat to others comfort and life!" he said in a rather drab voice.
It calls for a serious probe as to why by any chance a sane and "moral" man has to suffer when there are more (suffering) deserving people living out there happy and healthy lives? Deep within I could relate to it. The feeling I mean! It did not take me long to realize its not the pain of the suffering alone. Its more about self condemnation. When ever we see a man suffering the first thought that strikes involuntarily is the sense of relief , of course we feel compassion, a strong desire to help etc. but these more 'moral' feelings follow because we are relieved that we are not in that situation! Its built into our genes, coded into the very nature of intelligent life. And when we fall prey to one such disease or trauma our sense of relief  goes through turmoil and we find it hard to accept, how come we could be hit when we sailed un-hit so many other times?
By the law of religion: 
If we see what answer religion may have to offer or why we feel more pain, fascinates me!
Religion (all of them) teaches us to be moral, self controller, compassionate and charitable. It says the bad must suffer, the sinful must burn in hell and the selfish must bear the pain. And living by this code we every moment struggle to self-justify that we are righteous, selfless and helpful. This eternal struggle is but a friction to the very nature of our gene. Our genes are coded to be most selfish for survival. They affect out thoughts and behavior. We give up being ration and try to be a religious man not cause we know we should be more cause we are afraid of being the victim. And when we are the victim our trauma magnifies by many folds. To console, religion did an amendment with multiple birth theory and karma being calculated and carried over to next births etc. But that hardly explains why some one has to suffer while other get away with ill doing.
Law of Nature:
There are laws of nature which are universally the same for every one. does not discern people over money, sex, religion, dead, living or anything. If you exist in this universe the laws apply on you! Its a random choice. A random selection that one encounters a fortune or a misfortune. For example 10 people went for a hike, 9 survived but just one toppled over the peak to a fatal fall. Now what caused him fall? Gravity! and gravity was working on each individual out there on the top. But why only one has too fall? Its a random event if we look just by the law of nature.
              But if you take a bottom up approach and connect the dots we may figure out a reasoning why he had to fall and why he had a bigger chance of falling then others. The choices we make at any moment they affect the yield of the next moment. There ain't anything called completely random. Things are biased in a smaller sample, adding to a bigger pattern and each bigger pattern summing up to form another. However these patterns as of today can only be understood looking back, once the events have already occurred. So for us the why me part of the problem does not really going to help. If we think rationally we already knew why me.
Game theory explains:
Let us assume all beings in the universe are rational. Life is a variety of game. Where we make choices to maximize pay-offs. Pay offs like a better lifestyle, success, happiness, relations, social status etc. We deal with fellow competitors(humans). Now if we look at it we can find we spend maximum energy calculating and comparing the relative pay off. Comparison we make with other competitors. This nature tempts us to bias our decisions and hence we choose non optimized strategies just to land on a much less pay off than what we should have got. But over all prize in the whole game is constant so when some one looses because of a choice some one else must with on that move. And that's how exactly it all works.  So the best way to play life would be to device a strategy which is indifferent of other loss or gain and we always choose to maximize our own pay offs and make honest decision. This will improve the over all game condition.


Why me?
You cause you are a 'random' choice of the laws of nature
You cause your decision biased nature's random choice making your selection slightly more probabilistic
You cause religion does not really help neither being religious in defying nature's laws

Truly
Abinash