Thanks a lot for a confirmation of my view that relative marking is grossly inappropriate in the circumstances. I'm afraid that I'm not in a position to demand any guarantees, for I have no legal recourse if they simply ignore my demands. To cheat, or not to cheat, that is the question, unless they change their mind and the procedure of the test....

@mitsuko Which country is that?

The answer doesn't say "demand." It says "ask." Try this: "Professor, while I understand there are dire consequences for cheating, given the circumstances it seems likely that some will. If so, relative marking seriously disadvantages honest students. Could you please reconsider your marking decision?"

@Mitsuko, to cheat or not to cheat? Not. That's an easy answer unless you are someone who condones that behavior. If being honest puts you at a disadvantage then you still have your personal honor by not cheating. If personal honor means nothing to you, then cheat. The only question you need to answer is, what type of person do you want to be? And also, consider the consequences. Lastly, what mechanisms to detect cheating do the proctors have that you may not be aware of?

@CramerTV OP should never have been put in a situation where this question even arises. It is easy to demand not to cheat in such a situation, but unless one is so superior that one can blow any other student out of the water including any cheat helper, a grade in an important course being determined by ranking makes it a direct zero-sum game and creates an "all is fair in war" attitude. I would never advise to cheat, but one cannot ignore the moral conundrum and talk loftily about honour, it does not help the OP. Here, "honour talk" perpetuates the exploitation of the honest by the corrupt.

>> Which country is that? << It's Japan.

@BobBrown : The whole purpose of the test is to measure how good the students are relative to each other, and the results will be used to divide the students into small groups so that each group comprises of students of approximately the same level of knowledge. Then each group will be taught in accordance with the abilities of its students. So the grading on this test just has to be relative. This is simply why the test is conducted.

@BobBrown : What matters now is the position of each student on the list sorted by performance on this test. The test won't count towards my final grade, but I want to end up being in a group of good students. As you see, it makes sense to complain only about the procedure of the test, not about the grading system.

@BobBrown : And he may even add, " If, which I do not for a moment believe, a substantial portion of students cheated, I would see it by the average absolute score and the distribution of absolute scores. The test is held every year, and its difficulty doesn't really vary with years, so I have something to compare the statistics with. "

@BobBrown : How would you counter that? If I were to be brutally honest, I would respond to the examiner, " Let's be honest, okay? Your life is strained by the pandemic as you have to do a lot of extra work, so you won't do anything about the cheating even if you see a moderate shift in the stats as compared to the previous years. You have many other things to do, don't you? And will you really want to start a scandal about massive cheating? You'll surely elect to sweep the dirt under the rug, as otherwise your superiors won't be happy. "

@BobBrown : But I can't respond in this way, for obvious reasons. Who wants to alienate a professor who will grade you? Which brings me back to the original question, to cheat or not to cheat...

@Mitsuko - The purpose of the test, and the fact that it does not affect your final grade seem relevant to the question. I would update the question to include them.

@Phil : Thanks, I just edited the question accordingly.

@Mitsuko The fact that it does not affect the grade is important. It would have quite changed my response. If they have statistics from earlier years, they can indeed identify likely cheaters (it's not that difficult), at least suspicions for these. Second, if there are cheaters, then the non-top honest students will sit in similar rankings with each other. It's the top students who will be burdened with cheaters in their team. The whole consideration changes now. Also, the incentive to cheat now seems lower. The question is now really why you would want to cheat at all?

>> The question is now really why you would want to cheat at all? << The reasons are numerous. In a better group, you get a better instructor, a better and more stimulating environment, and an opportunity to make social connections with better students. Even if you are worse than them, you'll get motivated to catch up.

The practice here is that best groups get best instructors. Whom would you give the best English teacher - a group of lazy students or a group of students highly passionate about the English language? And the environment does matter. If you are in a group of good students, you will invariably become like them. Students take this test very seriously, and I do expect that some will cheat. And I don't want my place in a good group to be stolen by a cheater.

The statistics are from the previous years, i.e., for those students who are older than us and sat this test in the previous years. No one of those who are to sit the test this year sat the test in any of the previous years. So all the examiner can do with the stats is to say whether this year's cohort of students performed much better than the previous cohorts did. If he finds a huge difference, it will be obvious that massive cheating took place, en masse. But that's all he can deduce. I'm afraid he'll find some moderate difference and won't act on it.

Actually, the original version of my question clearly said, " ... the test is important because it affects, in some unknown to me way, the future division of the students into small groups. " So the role of the test was clearly stated in the original version of my question.

@Mitsuko Ok, so it's important, that's what matters. Well, you need to be very polite (yes, I know Japan;-) but make your case about how to ensure that cheating will not affect you adversely. If you are blown off, then the question is really whether there are any corrective committees that you can bring up your complaint to. But, first of all, make sure they are fully aware of the incentives. I used to have good success with "honour pledges" years ago. It does not work anymore. People can lie blatantly in one's face and, when found out, they unpack an "I didn't know". There need to be checks.

I myself gave an upvote to your answer because I believe it is grossly inappropriate to allocate students to groups based on a test on which anyone can easily cheat. Honest students get disadvantaged and end up being taught by worse instructors. I do not see how your answer should change in view of the fact that the test doesn't count towards the final grade. After all, I learn for the purpose of getting knowledge rather than getting grades, and I will get more knowledge in a better group.

Assuming your professor has even an ounce of academic integrity, they will have no issues finding a reasonable accommodation especially considering the circumstances. Sometimes they're managed by TAs who couldn't give a hoot, but usually someone notices when top students do poorly and struggling students do spectacular, and even more so when it's brought to their attention ahead of time.

@Mitsuko I agree that you deserve a strong group. What I suggested (of course I do not know how the mechanisms work in Japan) is that when it is not a grade that is decided but group, that the incentives become slightly different. The cheaters get together in the "top" group and everybody else according to their capability. If you are a top student you probably will then be more disadvantaged because you have to work with cheaters. Much depends on the actual cheating statistics, but the situation is then not quite as clear-cut. As for TAs, I have learnt from the weak ones, too. Good luck!