Calculating Degree of Separation and Probability

Question

If there are 18,000 people in a subset of people in the United States, what is the degree of separation from a random person in the rest of the population of 330,000,000 people?

And what is the probability or likelihood that one of the 330,000,000 will encounter one of the 18,000 in a given year, assuming everything is random? (I understand this is more difficult to estimate.)

If you are able to answer this question, I'd appreciate a commentary on how you arrived at the answer. Thank you.

Answer 1

The degree of separation, also known as the "degrees of separation" or "six degrees of separation," is a concept that suggests that everyone is, on average, six social connections away from any other person in the world. This concept is based on the idea that people are linked through a chain of acquaintances.

If there are 18,000 people in a subset and 330,000,000 people in the total population, the degree of separation can be estimated as follows:

Degree of Separation = log⁡(N)/log⁡(A)

Where:

1. N is the total population (330,000,000),
2. A is the subset population (18,000).

Degree of Separation = log⁡(330,000,000)/log⁡(18,000)

Calculating this, you would find the average number of social connections between a random person in the subset and a random person in the rest of the population.

As for the probability of encountering someone from the subset in a given year, assuming everything is random, it's challenging to provide an accurate estimate. The probability would depend on various factors, including the geographic distribution of the subset, travel patterns, and chance encounters. A simplistic way to estimate this would be to consider the ratio of the subset population to the total population:

Probability = Subset Population/Total Population

In this case, it would be 18,000/330,000,000. However, this does not take into account the complexities of real-world social interactions, travel, and other factors that could influence the likelihood of encountering someone from the subset.



Keep in mind that these are simplified calculations and real-world social networks are influenced by many factors that are difficult to capture in a straightforward formula.