Popular Tests to Assign People to Groups are Generally Bogus
From the Political Compass to the Meyers-Briggs Type Indicator (MBTI) these tests attempt to categorize people by their answers to a list of questions. In the case of the Political Compass, the number of questions is too few, and the questions are too binary to allow for a good assessment. The questions use too many words that lead those who read them to answer in a certain way. Words like "always" and "best" are superlatives and any thinking person will find themselves led to answer in a way that the test designer more or less wishes. They lead the responses. In the Political Compass, the bias is to lead thinking people toward the Libertarian/Left quadrant, through the use of superlatives in the questions.
Further, in both tests, and other similar tests, intelligent people can successfully predict how the the answers will affect the results. For the MBTI, for example, an intelligent person can often predict the results the test-giver is looking for and answer the questions in a way that will produce a result that produces a better fit. A salesperson, for example, will be expected to be an extrovert with high levels of self-confidence. So, by answering the questions in a way that presents the test-taker as such will naturally lead to a better result in terms of getting a job, the most used reason for taking an MBTI.
In some cases, attempts have been made to include prominent people in the results, even though they have never actually answered the questions. In those cases, someone will answer the questions as they think the prominent person would answer. The problem is that the biases of the person answering for another person will skew the results, since it is easy to manipulate the outcome for anyone with test-taking experience or knowledge of how the test works.
These tests are questionable, even when taken by a person who tries to answer questions honestly, but are completely useless if someone other than the person answers the questions for a person, based on whatever knowledge they may have. Such results are completely useless. For the individual who answers honestly about themselves, the tests can provide some interesting information about that person, who can reflect on why the results turned out as they did, based on the questions asked.
Psychological testing is a complex business, and designing tests is a very difficult thing to do. However, if one understands testing, it is relatively easy to write the questions in a way that will lead test-takers in the directions you want them to go, if that is your goal. Sadly, there's a lot of crappy testing out there, full of badly-written questions that expose the biases of the test designer more than it exposes the personality of the test-taker.
On a personal level, I have taken both the MBTI and Political Compass tests a number of times, both on a required and voluntary basis for the MBTI. I can position myself however I wish by answering the questions as I choose. A little thought is all that is required. I first got interested in this kind of testing while taking upper division courses in psychological testing to expand my knowledge of psychology. That is when I learned how easy it is for test-takers to manipulate these tests as they choose, and when I learned that their value is limited because of the transparency of the test designs.
Since it is so easy for an individual to manipulate the results, it's clear that someone taking the test for someone else can position that person as they choose. Only an individual answering honestly can get worthwhile results from any personality assessment test. Anything else is fraudulent and should be discarded as useless.
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They can provide some self-knowledge and can lead to growth and thoughtful change in some cases. When used for other purposes, however, they're most often of more use to the test-giver than the test-taker, unless the test-taker manipulates the results deliberately to match the perceived desires of the test-giver.
If you're an employer looking for a self-starting, results-driven, sales powerhouse who will follow your script, I can give you an MBTI result that will knock your socks off. Of course, they'll also be bullshit, but hey, I need the work! You'll probably hire me, and I interview really well, too. 
