It depends a lot on the type of objects and persons in your sample. There may be several ways to achieve what you are trying to but I am listing an approach I have myself used in the past and hence am familiar with in quite a lot of detail. Other users may mention innovative new techniques.
I will refer to the activity of choosing an item as "buying" but it can refer to anything --voting, hating etc. This approach is only valid for objects that associate similarly with the buyer's (or chooser's, user's etc.) psychology. In such a case a preference/ratings matrix can be a very simple and crude way to solve the problem. Here is how such an approach works:
Step 1: Data Gathering
- You would ask people to contribute objects they liked with a scaled rating (say on a scale of 10).
- In the "analysis" or "taste discovery" phase you would suggest them items that they haven't rated and ask them to rate them.
- Furthermore, you would ask them to group/tag the items into pre-defined categories.
Step 2: Analyze Correlation and R-Squared of buying tendencies
An example object-person ratings matrix may look like:
Object 1 Object 2 Object 3 . . . Object N
Person 1 6 4 4 10
Person 2 4 2 1 8
Person 3 8 9 10 1
Person N 3 4 9 2
You will then have to run a regression on this matrix to determine correlations and R-Squared between object-object pairs, person-object pairs, and person-person pairs. Repeat this analysis with the category-object matrix and then finally the category-person matrix.
Step 3: Interpret
If you can show that people who like A, B, and C also like D with a high probability (measured relative to other probabilities) then you can assume that another person who likes A, B, and C will also like D with a high probability. In some cases you can also measure likeliness coefficients --probability that objects will be liked/disliked given that another object is liked/disliked.
In cases where you cannot establish enough correlation between individual objects it may be possible to group/divide objects into hierarchies or genres (science fiction movies, Asian cuisine, denim outfits, swiss watches etc.) and then get correlation stats between those higher groupings. You can continue to hierarchise objects into broader or narrower groupings until you get meaningful correlations out. That is why we also collected category information above.
In many other cases, where no meaningful correlations exist, you will have to rely on network effects. For example, a person A may tend to follow person B's choices --regardless of the objects in question. You do not need to know if A is person B's friend/follower because the data you have collected will predict this pattern (if it exists) anyway.
- Small sample size (of either users or objects). See also, law of large numbers.
- Misinterpreting correlation as future prediction indicator --use both R-Squared and correlation to calculate probabilities.
- Misclassifying the problem --sort of obvious. Here I have assumed that objects associate similarly with buyer's psychology --if that is not the case, this approach may not work.