15.071 | Spring 2017 | Graduate

# The Analytics Edge

9 Integer Optimization

## 9.3 eHarmony: Maximizing the Probability of Love

### Video 1: The Goal of eHarmony

The slides from all videos in this lecture can be downloaded here: Maximizing the Probability of Love (PDF).

### Quick Question

eHarmony has a distinguishing feature, that makes it stand out from other online dating websites? What is this?

Explanation eHarmony was not the first online dating site, and while they ask users for personal information and charge a fee, other online dating sites do that as well. What distinguishes eHarmony is that they only suggest matches to users, instead of allowing users to browse other users' profiles.

Continue: Video 2: Using Integer Optimization

### Quick Question

In the previous video, we saw a small example with 3 men and 3 women. We defined a “match” as an assignment of each man to exactly one woman, and each woman to exactly one man. The optimal match in the previous video was to assign man 1 to woman 3, man 2 to woman 1, and man 3 to woman 2.

How many different feasible matches are there in the example with 3 men and 3 woman? (HINT: Another feasible match is to assign man 1 to woman 1, man 2 to woman 3, and man 3 to woman 2.)

Exercise 1

Numerical Response

How many different feasible matches are there with 5 men and 5 women? (HINT: First assign man 1 to one of the women. How many choices are there? Then assign man 2 to a woman - how many choices are there now? Repeat this until every man is matches to every woman.)

Exercise 2

10

20

50

100

120

150

Explanation

In the first case, there are 6 possible matches. The first man can be assigned to any of the 3 women (3 choices). Then the second man can be assigned to any of the remaining 2 women (2 choices). The third man is automatically assigned to the remaining woman. So there are a total of 3*2 = 6 choices.

In the second case, there are 120 possible matches. The first man can be assigned to any of the 5 women (5 choices), then the second man can be assigned to any of the remaining women (4 choices), etc. This gives a total of 5*4*3*2 = 120 different matches.

You can easily see how the number of possible matches gets very large on online dating sites!

On slide 4 of the previous video, we gave the following confusion matrix to predict compatibility between users:

 ACT\Pred 0 1 0 1030 227 1 126 92

### Quick Question

What is the accuracy of the model, according to the confusion matrix above?

Exercise 1

Numerical Response

Explanation

The accuracy of the model is (1030+92)/(1030+227+126+92) = 0.76

### Video 4: The Analytics Edge

Back: Quick Question

## Course Info

Spring 2017
##### Learning Resource Types
Lecture Videos
Lecture Notes
Problem Sets with Solutions