# Comparing two lists to measure for similarity

The problem I am trying to solve is finding the probability that two people are the same by cross-referencing the associates of the two people. For example, if person A is associated with the following people:

• Jeff
• Rick
• Jessica
• Mary

Person B is associated with the following people:

• Ryan
• Mary
• Dennis
• Scott
• Jeff
• Sharon
• Rick
• Larry
• James

So these two people have the following people in common:

• Mary
• Jeff
• Rick

How would I go about figuring out the likelihood that Person A and Person B are the same based on the common relationship with the three people above? There are three factors I can see right now, but I don't know how to weigh any of them:

1. Ratio of common associates (doubled because seen from both sides) over the total number of associates
2. Ratio of common associates over the number of associates for Person A
3. Ratio of common associates over the number of associates for Person B

I'm not a statistician, so I don't know if what I've presented is the correct way to solve the problem. Can anyone provide some guidance?

• Can you say a little more about your situation? Are you trying to detect if A & B are the same actual person? Is this something like you have two sets of lists, but the names were left off, & some of the information is missing? Eg, do you know that A doesn't know Ryan, or is it that you don't know whether or not A knows Ryan? Jul 25, 2013 at 3:25
• Yes, I am trying to determine if A and B are the same person. To be more specific, I am trying to match up authors of medical journals across different articles based on a number of variables (e.g., name, research organization, research topics, co-authors). The question I'm trying to answer is if author John Doe wrote article ABC and author John Doe wrote article XYZ, are these two John Doe's the same person based on the amount of parity for each of the factors mentioned (I will eventually need to combine these factors, but that is another problem :)).
– Mike
Jul 25, 2013 at 4:22
• The original post was describing how I might compare the co-authors of article ABC to the co-authors of article XYZ with the assumption that if a certain percentage of co-authors match between the two articles, the strength of the relationship between the John Doe's will increase. In my original example, A does know Ryan because they worked together on the research article. But one thing A does not know is if the Ryan B knows is the same Ryan that it knows. I am trying to determine the degree of certainty between A, B, and any of their associates based on how many of them are connected.
– Mike
Jul 25, 2013 at 4:23