Consider the following scenario:
Collection of user data from a community site similar to StackExchange reveals that certain users tend to "agree" with other users; e.g., when participating in the same posts, they tend to upvote or downvote together. Simultaneously, certain users tend to "disagree" with each other. Again, when they participate in the same posts, they vote the same.
An example of collected data might look like this:
thread1: upvotes: 8fsygfs // Each key (e.g., "8fsygfs") represents a user atw9g87 atw923swg87 34j2njk" downvotes: jne280n 892ned9 28hd0ye cjsnd09 02jd0d2 thread2: upvotes: 02jd0d2 8fsygfs 7dr4229 232c3f25 34j2njk atw9g87 atw923swg87 downvotes: jne280n 9ah8229 89h208d 28hd0ye cjsnd09 thread3: upvotes: 02jd0d2 9ah8229 838w32l 78awg2l 34j2njk downvotes: jne280n atw9g87 892ned9 28hd0ye
If we parse this data, we can extract the absolute number of times that a given user votes the same as the rest of the users.
34j2njk: // The users below have "agreed" with this user 8fsygfs: 2, // 2 times... atw9g87: 2, // 2 times... atw923swg87: 2, // 2 times... 02jd0d2: 2, // 2 times... 7dr4229: 1, // 1 time ... 232c3f25: 1, 9ah8229: 1, 838w32l: 1, 78awg2l: 1
There are a number of other ways to parse this data. Another example is to look at how often a user agrees with other users. Here I've set a threshold where users must participate in the same thread at least 3 times before we calculate how often they "agree."
34j2njk: // The users below "agree" with this user... atw9g87: 0.6666666666666666, // 66% of the time 02jd0d2: 0.6666666666666666 atw9g87: // ... and this user... 34j2njk: 0.6666666666666666, jne280n: 0.3333333333333333, // 33% of the time 28hd0ye: 0.3333333333333333, 02jd0d2: 0.3333333333333333
How might I approach this data if I want to establish "poles" that represent user behavior? For example, toward one pole you'd have a group of users who tend to agree with each other. Toward the other pole, you'd have a group of users who tend to disagree with the former group. In the real world, users would fall somewhere between. I'd like to create an index that represents where in the space between each user falls.
To be specific, I'm looking for exposure to any concepts that would be helpful in this goal. I'm not looking for anyone to approach the data for me. As a lay person, I'd like to know what terms, concepts and areas of statistics and math in general would be helpful to me in exploring this further.