It may be the case that you prefer other people to take the test, even if you don't want to take the test yourself, and that is the position of the whole population. What is the right thing to do then?

(Assuming sufficiently large population) I'll take the test if and only if I believe the others will take the test if and only if their (accurate) prediction is that I will take the test. With given assumptions this function returns true. I take the test.

What wins: personal preference, or this "circular altruism", preference about other people that not a single person accepts for oneself?

Whatever I want. I can have terms for 'wanting others to get what they want' and also 'wanting others to have what I want for them'. This is a simple matter of preference and not complicated more than any other preference by the newcomblike situation or 'timeless' reasoning.

Just be clear on the distinction of "wanting to others to get what they want" and "doing what others want because I can predict or otherwise know that others will give me sufficient utility iif I do". The motives described here have not included the former.