Well it turns out that a reasonable strategy is to find some fraction
and perform the following algorithm. Observe the "spectrum" of applicants
up to some predetermined fraction of the pool and then pick the next person
who beats everyone that preceeded him/her. The question now is what is the
fraction to observe that will maximize the probability that you select the
Ofcourse this way it is possible that you never see the best or it
is possible that you will already have passed the best and are doomed, but
nonetheless this is the method to maximize the probability.
For the very interesting application to follow, all you need is the
existence of this number. Assume that it can be calculated.
The Dating Game
You're young and waiting. How long should you wait?
- You HAVE to find you're true love. If you don't, FAILURE!
- Strange assumption as this may be, you don't "see" all the "applicants"
- Immediate notification is necessary. If you dump (or get dumped) then its
bye-bye to that be-be.
- You have some approximation of the number of people you will date.
- You date FAST, cause obviously there is some loss to waiting too.
- BUT WAIT, this is exactly the interviewing problem!
- The strategy is date a while, sample and see. When you have used up your
"training" sample, its time to get into marriage and settle
down mode. If someone
now comes along that beats all your ex's, then heck, marry her/him.
- It turns out that a simple calculation shows that the optimal fraction
is about 1/e, roughly 37%. This is magdon's "one over e" theorem for
what does this mean?
- The average person expects to date at a rate of say
12 people a year for about 10
years (rough estimates). i.e. 120 people, so about 40 people "should" be
sampled before even thinking that rockets are firing.
- I ask you, is this not the strategy that most people follow unwittingly?
In fact we can say more. We can categorize people into those who are in the
pre-1/e stage and those in the post-1/e stage...hmm...the "so called" people
who are ready to settle down...lest I get in more trouble, I shall say no
mail comments to malik
WARNING! Some people claim that they can identify their TRUE LOVE on the
spot. BEWARE of such FOOLS!
One must also take care to abide by The Magdon-Pregs Wild-Timid theorem.
All this analysis decays when one reaches a point in one's life
decides that the best is not necessarily the only acceptable solution.
Sad as it is to say,
perfect is not a practical word.