Jaccard Similarity — A Simple Example

For a given term (say fraud) in a given year, you have two separately-trained Word2Vec models — one on Democrat emails, one on Republican emails. From each you pull the top-10 nearest-neighbor words to fraud. Jaccard asks: how much do those two neighbor lists overlap?

Notice the similarity scores are thrown away — only the words matter ($w$ for $w, s$ in ...). It's purely set membership: is a word in both top-10 lists or not.

Simple example

Say for fraud in 2020, with $k=10$:

Now compare the sets:

1. ∩
   Intersection (in both) voter, claims → 2 words
2. ∪
   Union (in either, counted once) the 10 Dem + 10 Rep minus the 2 shared = 18 words

How to read it

1. 1.0
   $J = 1.0$ → identical neighbor lists. Both parties surround the word with the same associations → convergence / shared meaning.
2. 0.0
   $J = 0.0$ → zero shared neighbors. The parties embed the word in completely different contexts → maximum divergence / polarization.
3. 0.11
   The example's $0.11$ says Dem and Rep talk about "fraud" in largely different terms — Democrats frame it around debunking/suppression, Republicans around mechanisms of alleged cheating.