Mathematical search of true love

1. SOULMATE
BY: NSUBUGA IVAN
From: ACIT global by Manuel Brenner Phd (University of Heidelberg)

2. Introduction
• Soulmate is a person ideally suited to another as a close friend or
romantic partner.
• The word first introduced in the 19th century and recorded first in
1882 in the letter written by poet Samuel Taylor Coleridge, “To be
happy in married life…….you must have a soul-mate” he wrote.

3. Continua……….
• The world is a rich place of opportunities waiting to be discovered, of
actions to be taken and choices to be made.
• Humans, just mere mortals having to navigate this world with partial
and biased information and take decisions under uncertainty.
• Taking many decisions quick and dirty, without too much time to
consider them in-depth and without having the luxury of looking at
them from all sides.

4. Continua………….
• This is especially true if we have to act in an environment full of
competitors, all pursuing their own self-interests and all struggling
with similar uncertainties:
• Be it when looking for an apartment in a popular city, looking for the
dream job, or waiting until you finally meet your soulmate and get to
live happily ever after.

5. EXPLORATION-EXPLOITATION TRADE OFF
• Fundamental concept in decision making.
• It’s the balancing act between two opposing strategies:
• Exploitation involves choosing the best option based on current
knowledge of the system(which maybe incomplete or misleading).
• Exploration involves trying out new options that may lead to better
outcomes in the future at the expense of an exploitation opportunity.

6. Continua………..
• Finding the optimal balance btn these two strategies is a crucial
challenge in many decision-making problems whose goal is to
maximize long-term benefits.
• Using the famous secretary problem as an example.

7. FAMOUS SECRETARY PROBLEM
• Say you are looking for a secretary, and you have 100 days scheduled
for this task, at each of which you can lead one interview with a
potential candidate.
• Assuming, every secretary that you interview would instantly agree
to start working for you, but you need to make a decision right after
each interview, and if you don’t hire the candidate, there is no turning
back.

8. Continua…………
• Given these conditions, what is the optimal policy to pursue in order
to find the best possible secretary?
• The perhaps surprising result is that you should start by interviewing
37 secretaries without hiring anyone, and then continue your
interviews until you find one that was better than all the previous 37
candidates.

9. Continua…………..
• Mathematically this can be proven that this policy maximizes your
chance of finding the best possible applicant, which also lies at 37%.
• Rephrasing this in terms of the exploration-exploitation dilemma, you
should start out with an exploration period that lasts for Y/e (where
e=2.71828… is Euler’s constant and Y represents the limited period of
time ).
• Of the total period, and in which you force yourself to not make any
decision, even though some candidates might already seem perfectly
suitable

10. Continua………….
• This of course only makes sense if you really have 100 days to spent
and no additional incentive to be done as quickly as possible, and are
looking for the best possible candidate.
• Then after the exploratory you use your opportunity to hire the
candidate that impresses you more than everyone before
(exploitation).

11. Continua………
• To make a perfectly unromantic transition, the secretary problem is a
bit like dating. After all, there is plenty of fish in the sea, but only
limited time.
• The problem: mathematical assumptions of the secretary problem
don’t seem to translate too well to dating at first glance.
• We usually don’t know for how long we will be dating in total and
how many potential partners we have, and it is difficult for us to
objectively rank the quality of a partner.

12. Continua………………
• We learn much along the way, and sometimes there is in fact a
turning back (although you can ask yourself how many people you
know that successfully got back together with their ex-partners).
• Dating and mating have evolved for a reason, evolutionary
psychologist David Buss points out, we have evolved sophisticated
strategies to quickly assess potential mate value and to judge if a
respective partner will have the resources and genes to increase the
chance of healthy and surviving offspring.

13. Continua……………
• And indeed we are quite good at picking up many important often
unconscious cues already in the first minutes of meeting someone
new.
• And while now we could potentially date until we are 100, the aim of
many marriages is to build a family, which puts additional biological
constraints on a realistic time period we have for exploring our
options.

14. Continua…………….
• Finding your soulmate is not easy, assumption: you want to be
married by 32-35 (which is the average age for women and men,
respectively), and start seriously dating around 18.
• Then you have some 15 years to roam around living the single life.
• Mathematics then teaches us that should explore dating for at least
15/e=5.3 years and then settle on the partner that was “better” than
everyone else before, whatever that means.

15. Continua……….
• Sorry to break this to all the high-school sweethearts, but optimal
stopping theory is not on your side.
• Mathematics shows us we shouldn’t exclusively see exploring as
taking a risk, but also as a means to find places in our lives where it
might be more optimal to stop.
• And who knows, if we play by this rule we might even end up with
our soulmate, and live (with 37% probability) happily ever after.
• Good luck with finding ur soulmate.

16. The secret formula for finding true love,
powered by optimal stopping theory.

17. THE END THANKS FOR YOUR TIME