It is not a relationship blog or anything even close to it. Just math. Pure applied math.

Assumptions:

  • For this experiment we take in account only M2F relationships. I support sexual freedom to everyone, just the math is easier this way sooo…
  • One sided relationship doesn’t count as a relationship. Sad. I know :(
  • Self loving is also not a relationship. LOVE YOURSELF
  • Number of guys and girls are considered equal as a fair assumption.
  • A love triangle needs at-least one of the edge to be homosexual so not considered in our modelling.

Notations:

  • X → Random Variable for number of relationship of girls
  • Y → Random Variable for number of relationship of guys

Lemma 1: E(X) = E(Y)

Proof: If we model each individual as a node in graph, by our straight world assumption, the graph is bipartite and we can change all edge as directed going from a girl node to a guy node.

∑ X = Sum of out degrees of all node = Sum of in degrees = ∑ Y

Also, as ∑ 1{X = x} = ∑ 1{Y = y}, i.e. number of individuals in both gender is same, we have E(X) = E(Y).

Now for the real calculation,

For every girl i, X_i is the number of relationships she has been in. For every guy j, she has been with Y_j is his count. So, her perception for average girls a guy dates is

i.e average of Y over all the guys she knows about i.e. X_i .

To calculate this quantity as an expectation, we need to sum this over every girl and every guy she has dated, i.e.

Step 3 because if we sum all the instance i that has edges with j, it is same as the degree of j. Now, from the lemma E(X) = E(Y)

The last part follows from the inequality E(X²) ≥ E(X)² and equality is in the case where variance of X is 0, surely not a case in dating world. As Y and X are interchangeable, the calculation for other general also follows.

E(average relationships of your partner) > E(your average relationships)

So, WE NEED TO TALK. Not about how many partners or relationship history, but math and science and it’s beauty.

Peace.

Tl;dr : When calculating average for partners, a partner with higher degree is calculated by partners multiple times and hence the abnormality in the averages.

Reference:

I highly encourage readers to try working this proof by themselves in details, and in any doubt, I will be happy to answer personally or in comments.

Originally posted on Medium