About Me

!nversed Poignancy!

...I am an eclectic amalgamation of many seemingly paradoxical things. This can be exemplified in both my seemingly endless persistance on many topics and arguments, as well as my careful cautiousness on other topics and arguments. This is largely due to how astute I am of the topic: more knowledge, more persistant; less knowledge, obviously more cautious. I also have times of obsessive compulsions regarding certain things (mostly just my thoughts, however)...

Life and Death

!nversed Poignancy!

Life

An assembly

Possibly impossible

Perfectly interchangeable..

Death

That lives most upright

Beyond the unspoken

Neither a squiggle nor a quibble..

She and Me

!nversed Poignancy!

She

A daffodil

Tyrannizer of me

Breaking the colors of dusk!..

Me

The rising sun

Infringed with violations

The impurity in the salt..

Love and Poetry!

!nversed Poignancy!

Love

A puerile desire

Buried in the heart

Never leaves..

Poetry

Sentimentally melodramatic

Cursively recursive

My thoughts idiotic!

The Partner Theory

Scribbled by Bharath C On April 02, 2016
“Time flies, whether you’re wasting it or not.” 
― Crystal Woods, Write like no one is reading 
Prologue
Its truly unbelievable that I haven't been up with blogging for almost 6 years now! *Phew!* Infact, its astounding that I had almost forgotten that I even had a blog existing... It was virtually into its dusky Schrödinger cat's phase of being alive-and-dead.. until I received a note from blogger.com that there are over 300 comments that are requiring my moderation(!).  Alas!, a tiny chunk of the author in me died right there; how did I not find a sense of internal deviance of not having blogged for such a long time? I wondered, pondered and ruminated. For the uninitiated, I felt that the aura of the IEDs (Idiotic Emission of Thoughts) have died upon me.. but, as expected, the utter idioticity in me sprung up and I decided to write some non-sensical stuffs backed by some spurious math.

So, let's get the inkling rolling...
Well, yes! while, 6 *long* years seem eons ago, it does also mean that I have grown eons-over. Not to mention that the packets of advice that are showered upon me have moved from being "Choosing the path of right espouse in life" to "Choosing the right spouse in life". Needless to say that, I have been overwhelmed by people showering advices over the intricacies of how one's partner needs to be chosen. So, in this "come-back" blog, I thought I should discuss my IED, which I term - "The Partner Theory". 

Let's start with some basics.. From a thoughts of a birdbrained mind(like mine), finding the best partner seems a very "apprentice"ing term, the whole concept of this ritual is quite equivocal..  It’s much stronger than simple good platonic friendship, but at the outset doesn’t seem to be anywhere near a romantic relationship. It seems all-easy with a simple "match-the-following" algorithm, but, at the same time, there is a deeper "Theory" in it that lies unexplored for a sobel soul like mine. So, yesterday night, as I was putting myself to sleep, I was trying my best to somehow mathematically slot the pareto of this process; Urgh, yes. my thoughts around this might not be perfect (So, let me place a please-dont-try-it-at-home caution)–but lest assured, I'd say that my solution would be pretty good for such a really difficult problem.

Ok, so for the sane sake of defining the problem - let me first define my notion of "best partner problem", essentially, the aim is to find the "person" whom you think would meet your criteria for a "propose" action, but, that's not it.. the action also requires a mandatory reaction phase of "reciprocation".  Simply put, your aim is to search for your “best partner” by dating various people. Your only goal is to find the best person willing to “nod” for your “ayes” and any thing less is a failure. 

Hmm. So, let's move on and define the assumptions and constraints for this problem
  • Let C = {c_1,c_2,c_3,...c_k} be the set of potential candidates (not a bad term at all, I think. Candi-date(?) ) for the "best partner" tag for a person P
  • It goes without saying that C must be a type of non-concurrent idempotence,wherein, is allowed to date only one candidate at a time (not a bad assumption, I suppose)
  • For each pair (P, c_i), there is exactly two possible outcome - {0,1}. 0 for rejection and 1 for selection.
  • The outcomes are irreversible and non-repetitive. So, if there's a rejection (either way) the decision cannot be reversed
  • The set is countably-finite. Which means that you can date only a finite set of people during your lifetime (quite an important clause, I think :) ) 
  • For each pair (P,c_i) there exist a score function S(c_i | P) = S_(i,P) which is a grade that the person P assigns to the candidate c_i
  • Goes without saying that the grading is relative, which means, as you date people, you can only tell relative grades and not true grade. This means you can tell the second person was better than the first person, but you cannot judge whether the second person is your best partner. After all, there are people you have not dated yet.
Now, let's see the plausible naive strategies that can creep-in.
1.         Early picking : Well, its definitely not a case of "early bird getting the worm" See, if you pick someone too early, you are making a decision without checking out your options. Sure, you might get lucky, but it’s a big risk.
2.         Lazy stalling : Again, if you wait too long, you leave yourself with only a few candidates to pick from. yes, surely a risky strategy.

So, as always. It boils down to a static two player game [1] . The optimal strategy of a this would be to lock yourself into the search for ordinately finite interval and then hold the best match as (s)he comes along. But, there's a bigger trick here! its quite ambiguous as to how many people should you reject? 
Well, with a simply math, it turns out to be proportional to how many people you want to date, so let’s investigate this issue.

To make this concrete, let’s look at an example for someone that wants to date three candidates, so C = {c1,c2 and c3}. A naive approach is to select the first relationship. What are the odds the first person is the best? Yes! It is equally likely for the first candidate to be the best, the second best, or the worst. This means by pure luck you have a 1/3 chance of finding best partner if you always pick the first person. You also have a 1/3 chance if you always pick the last person, or always pick the second.

Can you do better than pure luck?

Yes, you can.

Consider the following strategy: get to know–but always reject–the first candidate. Then, select the next candidate judged to be better than the first person.

How often does this strategy find the best overall partner? It turns out it wins 50 percent of the time!

For the specifics, there are 6 possible dating orders, and the strategy wins in three cases.

(The notation First date=c3, second date= c1 and third date = c2 means you dated the worst candidate first, then the best, and then the second best. I marked the candidate that the strategy would pick in bold and indicated a win if the strategy picked the best candidate overall.)

  First Date
 Second Date
 Third Date
 Outcome
 C1
C2
C3 
Loss 
 C1
C3 
C2 
Loss 
 C2
C1
C3 
Win 
 C2
C3
C1 
Win 
 C3
C1
C2 
Win 
 C3
C2
C1 
Loss

You increase your odds by learning information from the first candidate. Notice that in two of the cases that you win you do not actually date all three candidates.

As you can see, it is important to date people to learn information, but you do not want to get stuck with fewer options.

So do your odds increase if you date more people? Like 5, or 10, or 100? Does the strategy change?

The answer is both interesting and surprising.  From the example, you can infer the best strategy is to reject some number of people (k) and then select the next person judged better than the first k people.

When you go through the math, the odds do not change as you date more people. Although you might think meeting more people helps you, there is also a lot of noise since it is actually harder to determine which one is the best overall.

So, essentially, to cut the long story short. Here's the summary of the best approaches
(i) Keep the candidates size as small as possible. (greater than 3 preferably, but, be aware that the as the size increases although the odds doesn't change, it does make rejection-selection problem much difficult as you need to hold-in a lot of prior information
(ii) If both of you are first-timers. Its better to talk a lot and decide on nothing. Perhaps, even if you really like the person, its always good to let them know in true Schwarzenegger style that.. "You'd be back" after assessing few other candidates (its better this way for both the folks, you see)
(iii) If only one of you is a first-timer. Its better to go with the choice of the non-first timer (this shoots your chances to over 60% when you do the calculations right)
(iv) Don't worry if you are an "early victim"
(v) If you are experienced-bee, while the better strategy for you seems to be to ensure that you keep the first-timer to non-first timer ration to as close to 2/3 as possible.
(vi) Mostly importantly, any one of you could reach out to me to seek more details on the calculations.. :D



6 Thoughts have been Sprinkled!, Your Take? :

Post a Comment

Post a Comment

Bookmark and Share