The more I think about this question, the more I feel that the way you interpret it is far more telling of what kind of person you are than your actual answer to it. In my opinion, the question is deliberately framed at least somewhat vaguely to allow for that kind of interpretation.
In the past I’ve kind of likened this question to the little psychological test: “finish the sentence: If the cuckoo won’t sing ___”, (which of course those who have read Majikoi would be familiar with - not sure about the prevalence of this elsewhere in society nor do I particularly care.) I was somewhat dumbfounded when one day my friend answered with “if the cuckoo won’t sing it’s probably fucking asleep, so just wait a while until it wakes up.” I had of course considered such things when answering myself, but had automatically factored it in to my answer and done my best to give an actual answer (not to say that his answer is actively invalid or anything), and it didn’t really occur to me that other people might not do so. It’s similar to the “wait until it does” answer but with a kind of nuance that tells you that he’s a bit of a jackass (which he is - not that there’s anything wrong with that.)
My assertion is that these question are intentionally vague and therefore in order for them to be fair, one has to answer them without further context. Of course, I would also assert that a demand for further context is itself an answer of sorts, but it’s not one I personally like because I think that you’re supposed to fill in the blanks yourself.
I even have a friend (my dumbass cuckoo is asleep friend) who puts the human race above the earth - which in the context of Rewrite would make him a Guardian supporter and therefore choose “Myself” to change, but since he interpreted “The World” as the human race, he chose “The World” to change. This is of course in opposition to my interpretation of “The World” to be my immediate to my not-so-immediate environment, including the variables but not limited to: society, culture, literal environment, etc, with something of an emphasis on the “literal environment” factor. So even though he and I strongly disagree on the issue in contention in Rewrite, our final answer is the same.
Is the “power” you have fantastical in nature?
To what extent can you control the change of the thing you’ve chosen to change?
How much “power” is it, really?
Can you really change one without changing the other? If not, is the question invalid or fundamentally flawed?
What is “The World,” exactly?
Hell, what even is “Yourself”?
It’s a very difficult question to discuss, considering that with the massive potential difference in interpretation that some people aren’t even really answering the same question in effect. But I think it’s a very valuable discussion to have, mostly in developing your own ideas in lieu of changing other people’s minds like you’d hope for in most debates or arguments. I think Rewrite itself really reflects the kind of impact the ideas this question challenges in it’s answerer, considering the massive changes Kotarou goes through between different routes, especially Akane’s route (which is really the only one where he takes a massively different stance from his usual, considering that in Chihaya’s route he refers to “we”(Gaia) as “the bad guys.”) Kotarou was naturally a fence-sitter on this issue this whole time which is why he is drawn to “I don’t know”, even when that’s not an option actively supplied to him. But in different routes where he’s had ever so slightly different experiences leading up to the choice that influence his mindset ever so slightly, he answers differently as a result. Knowing and changing his mind on the issue of this question does have very real effects on who Kotarou is as a person. And I’d like to point out that only in Shizuru’s and Akane’s routes - the ones where he chose an actual side - does salvation happen, and his actions are directly related to his answer. In Akane’s route he changes the world in a very obvious way (a few times, actually) and in Shizuru’s route he changes himself in a very literal way, right at the end.