Can I use matching instead of random assignment to achieve a quasi-independent variable? I know that textbooks tell us matching is an alternative to random assignment when it comes to quasi-experimental research. It allows us to make treatment and control group similar to each other.
However, another question arises: Can't I use matching not just for that but also to actually achieve quasi-independent(or non-manipulated if you will) variable?
For example, I want to see the effect of party membership on survey score. However, it's impossible to manipulate party membership variable in reality because of numerous reasons, so it should be regarded as a natural trait. If I wanna acquire treatment and control group which are similar to each other except for the party membership only, I randomly assign samples to treatment and control group, and the ask them their party membership, and then finally leave the same number of sample of each party membership category for both treatment and control group.
I tried to support or find a rationale for my idea, but I couldn't. Anybody has some knowledge or opinion on this? Please help.
 A: Using a randomization unrelated to the content of your study is called the instrumental variable approach. Try looking into that.
Your example won't work as you've described it. Let's say Party A has a higher average net worth than Party B. You want to create two groups that are equal on net worth but differ in party affiliation. When you randomize into 2 conditions, 1 and 2, it is true that what you are left with is two conditions, 1 and 2, that should have equal average net worth. Now you want to sample one party from each condition, so you leave all Party A people in condition 1 and all Party B people in condition 2, and throw out the rest.
The problem is that Party A members (even just those in condition 1) still have a higher average net worth than Party B members. Essentially what you doing is randomly throwing away some members of Party A and some members of Party B; doing so doesn't change the distribution of net worth in either party. You need to use strategic matching (e.g., propensity score) to throw out the right members of each party. An unrelated randomization wont help using the matching approach.
