Coding Social Influence Logistic Regression I am fairly new to regression modeling and was hoping to get some help.  Forgive me if this is has been asked before, but I couldn't find anything (maybe I was using the wrong keywords)
I have a dataset where I am attempting to answer the question: How much do a Person A's friends behaviors influence Person A's willingness to do action X?  The data from the friends (predictors) looks like:
Does best friend do X? Yes/No
Does second best friend do X?  Yes/No
Does third best friend do X?  Yes/No
The outcome is Person A performing the action (Yes/No)
I was hoping to fit a logistic regression model, but  I am having trouble coming up with a way to code the predictors, however.  
If I treat the predictors as separate variables, I get strange results (i.e. second friend is highly significant but not first.)  I think this is probably because there is high correlation between them?  Further, there is a fair number of observations that don't list 3 friends (~25%) which can't be used in such an analysis.
If I collapse them into one proportion (What proportion of the friends do action X?) the results are pretty clean, but I lose information about the ranking.  
Does anybody have a suggestion of a way of coding that will preserve more information?  I am hoping for something that will preserve the ranking of the friends.  Thanks for the help!
 A: 
If I treat the predictors as separate variables, I get strange results (i.e. second friend is highly significant but not first.) I think this is probably because there is high correlation between them? Further, there is a fair number of observations that don't list 3 friends (~25%) which can't be used in such an analysis.

Looks like you're having a hard time finding the right representation. If you tried a linear combination of features, you could also try a quadratic other combinations of features (e.g friends). 
Or, what if I told you that you can do this automagically?
You could train a neural network with one hidden layer. These are universal function approximators: https://en.wikipedia.org/wiki/Multilayer_perceptron
There are many implementations.

If I collapse them into one proportion (What proportion of the friends do action X?) the results are pretty clean, but I lose information about the 
  ranking.

If you need to rank the features, then compute the derivative of the outputs, according to the inputs. See for example: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.54.4570&rep=rep1&type=pdf
