Suppose you want to give free trials to Amazon Prime but only want to give the trials to users who are most likely to subscribe since giving free trials to everyone would be expensive. What would be a good response variable for this problem? There are two flavors of Amazon: Amazon Prime and "Free Amazon". The goal is to target the most likely people to convert who use "Free Amazon". Would giving a survey and asking the respondents to rate their enjoyment of Amazon on a scale of 1-5 be a good proxy for a response variable? Would running an ordered logistic regression model be a good approach using this derived variable?
Not sure I fully understand the question. If the question is how to choose the sample of people to offer the free trial, I would start by analyzing the properties of customers that paid the service and use it regularly (the best measure of customer satisfaction). Then you can build a classification algorithm that uses the same input variables, to predict how likely is a new customer to enroll in your paid service after a free trial.
Possible approach to this problem is to find some data about individuals that took free trials for something else (but similar to Amazon prime) and then make binary variable wheather they have subscribed after trial. Then you run probit/logit and get the model which assigns probability of subscription to individual based on some of his characteristics. Then apply this model to your potential trial recievers and give trials for those of them for whome estimated probability will be the highest.